In a sidebar on Handbook: House Marik, page 37, it notes that the ComStar War of the 2800s marked a low point in League-ComStar relations. But for centuries the League and ComStar have maintained close ties.
It specifically calls out Elisabeth and Thomas (fake Thomas though that wasn't publicly known at the time of that book) as two Captain-Generals who had ComStar schooling, contacts and influence. Then it says "though some claim they have advanced ComStar's secret agenda."
So the allegation is that she did advance ComStar's agenda. But it's not definitive. It sounds like there are people who think she did.
The same book notes that in Elisabeth's rise to the throne, her biggest competitor was Admiral Lloyd Marik-Stanley. Who at that time had already moved into the palace and had enough support to make a real go of it. One of Lloyd's biggest talking points against his rival was her close proximity to ComStar and he drew a crowd based on anti-ComStar rhetoric. He appealed to the anti-ComStar crowd in the League at that time (The ComStar War happened in the same century).
She ended up forming an agreement with Admiral Lloyd-Marik that would see him be the FWLM Commander-in-Chief while Elisabeth handled non-military affairs. This lasted 6 years. It was seen as a way to avoid a civil war. Eventually Lloyd died fighting and Elisabeth had sole control.
What Elisabeth is best known for is listening. Particularly on military affairs, in which she had little experience. She assembled smart people around her on various topics and listened to what they had to say. Handbook: House Marik calls this out and her charming personality as why she is recognized as one of the most beloved Captain-Generals. It says everyone from the lowest infantryman to the highest Duke felt like she would listen to them.
She also listened to Parliament and kept them informed, she had a good relationship with Parliament, a stark contrast to many other Captain-Generals.
My biggest takaways from all that are:
1. She was accused by some of advancing ComStar's secret agenda. But obviously if she did it was covert enough that the weight of history remains uncertain as to whether she truly did this or not. Maybe that was the point, because 2...
2. She arrived on a scene close to a low point in League-ComStar relations, with a strong anti-ComStar rhetoric in the League.
3. Her reign is best known for listening to others. Not ruling by fiat, not strong-arming the Parliament or the military. Just the opposite, she listened. So she didn't enforce her Will upon the Parliament or the military very much.
4. She did sign the Home Defense Act. Allowing provinces to hold back a large percentage of their troops for the defense of the province rather than the defense of the realm as a whole. This is regarded in the book as her one big mistake, because of how it much of a pain that law would become for all of the Captain-Generals after her. At the time, the book says, she saw it as a minor concession to Parliament and the nobles, not understanding the true implications.
So I read all that and feel like she was a good negotiator and moderate Captain-General who did a good job of getting everyone to work together and listening. Rather than try to strong arm the Parliament or the military. Given her leadership style she wasn't a great focal lense for ComStar's agenda....
Except she was, because all ComStar wanted was for the Great Houses to continue the barbarism, to continue to grind each other down until ComStar could sweep in and be a savior. During her reign there was plenty of fighting and even a few Marik victories of note. She helped facilitate that. She also probably helped to mend/recover from the low point in League-ComStar relations during her years as Captain-General.
Personally, I think in the eyes of ComStar, the best thing Elisabeth Marik could do for ComStar was to help mend things with the FWL. The ComStar War was rock bottom and that seemed to linger for a while. While Elisabeth Marik sat on the throne, relations seemed to normalize. ComStar was playing a careful balancing game in this era. They were advancing their own agenda(s) largely by virtue of controlling certain things (HPG communication for instance) as well as some degree of manipulation of events behind the scenes.
A big chunk of what ComStar was doing in this era was also just standing aside and letting the Great Houses continue to tear each other down during the 3rd Succession War. They were prepared to wait for humanity to truly bleed out, so that they could sweep in and be the savior. It was a long game and a slow game. This was prior to the Helm Memory Core, prior to the creation of the FedCom. The plan looked like it was working. The landscape looked pretty bleak for humanity during the 3th Succession War. ComStar was striving to keep things moving in that already-established direction. They wanted the downward slide to continue.
If Elisabeth Marik's reign had been defined as a era of ComStar puppetry, that could have further driven a wedge between the FWL and ComStar, maybe doing horrific unrecoverable damage to that relationship, perhaps to the point that ComStar was permanently booted out of the League. They couldn't have that.
In that time period it feels like ComStar's biggest agenda in regard to the FWL is just to calm things down, to get back on the League's good side, and that seems to have happened. If that was ComStar's agenda in the FWL at the time and Elisabeth Marik helped facilitate that, then she was successful.
As part of that, she had to dispel the fears of Lloyd Marik-Stanley's supporters, that she was just a ComStar puppet. That rhetoric apparently almost started a civil war, it reads like Lloyd had enough support to really make a claim on the throne. So Elisabeth Marik had to be very careful not to prove Lloyd correct.
Final thought. You call attention to her sudden claim to the throne. Her sudden appearance, with documents. My read on things is that happened because ComStar was afraid of how much worse League-ComStar relations might get if Admiral Lloyd Marik-Stanley had indeed become the Captain-General. Relations were already quite terrible and he had a notable anti-ComStar attitude and had openly spoken out against ComStar and became a rallying point for like-minded people. I think they wanted to blunt Marik-Stanley from becoming Captain-General. So they propelled another claimant into the mix. It had to be someone willing to normalize relations with ComStar, but to avoid a civil war it couldn't be someone who was obviously ruling as a ComStar puppet.
