I think this argues against them going. If 5 regiments and some warships is "inconspicuous", then the entire Ice Hellion Touman will just be a blip on the radar. There has to be at least some suspicion that the Ice Hellions are going to slam straight into a brick wall and never be heard from again.
The Dragoon compromise made sense.
The Clans needed intel, and the limited role IntelSer was allowed to play wasn't giving them enough.
But many Clans wanted to attack anyway. That is why the Dragoon compromise was reached. It enabled the Wardens to say that SOMETHING was being done and it was too sensible an idea for the Crusaders to dismiss it even though it was simply a delaying action.
The Hellions, regardless of what they brought, or what their fate may be, blows that arrangement out of the water. They could rush in and be destroyed...they could bring a single Galaxy and enact a direct strike at Terra. They could play it smart...wipe out the forces on the worlds they bypass, make use of their WarShips, but establish a space based logistics network with mobile factories and refineries rather than establish an onworld presence, and make use of abandoned SLDF bases for repair, rest and refit. Or they could squander their strength by trying to hold worlds they conquered.
This is, after all, around 3005 when new 'Mechs were kinda rare within the IS and many were held together with spit and bailing wire. OK...an exaggeration but we can't really say how well the Hellions would do because it depends on the tactics they would use and the numbers they would bring.
The important impact is on the rest of the Clans. Regardless of the Hellions, the secret is out. The Clans won't care that the Inner sphere might learn nothing. They might learn everything.
The Hellions might very well be censured. But they won't just be "let go"....not least because the Hellions in this scenario aren't asking. The Clans will have to assume the worst case scenarios - that the Inner Sphere will learn all about them. Or that the Hellions will take Terra and become ilClan.
If the Grand Council were to authorise some sort of "go as long as they don't blab" deal, other Crusaders will ask..."Why them and not us?" and will go anyway. In short...such a deal is impossible because it voids the Dragoon Compromise.
If they don't authorise such a deal, the Crusaders will say "The invasion you didn't want is here anyway. You cannot stop them. And we will be joining them. Stay here if you want. One of us will be ilClan and all of you will be fodder."
A Hellion invasion of the Inner Sphere may or may not be stopped. It may result in the Hellions becoming ilClan. It may not. It will, however, result in multiple Clans attacking the Inner Sphere, at most two years later. Most likely, within six months of the Hellions act becoming known.
Even if the scenario you posit is true, that also prompts an invasion because the prize is Terra and the ilClan.