Not exactly . . . the Ebon Keshik answers to the Grand Council, having risen above Clan loyalties (supposedly) . . . they guard Katyusha City, Prinz Eugen and I think Alex/Nick's flagship? They will respond to the ilKhan as the commander of the Clans under the martial code, but its questionable as to how much he can order them about or if they even leave the above mentioned places. For instance, Showers (first ilKhan since the Omni trials) had a Jaguar bodyguard rather than from the Ebon Keshik. Ulric Kerensky, who was elected back on Strana Mechty, did not return to the Inner Sphere with the Ebon Keshik- rather he used the Wolves Golden Keshik. Osis also had personal guards from the Jaguars rather than the Keshik . . .
To further my answer about the 'shadow' . . . it would not be long before another Clan absorbed the Jaguars- or say a de facto absorption. The other Clans did not wait for Osis to fall IIRC before they started nibbling at the edges of the Jaguar holdings. Say they fought Serpent to a stalemate and offered them hegira which left some remnant of the Jaguars alive. They had WAY more territory than they could adequately cover and so all those notes about what production & resources the Jag off of Huntress is lost. Asa Taney of the Ice Hellions and a few other Home Clan leaders had made noises about absorbing the Falcons & Wolves after the Refusal War . . . unlike that period where two Clans were sure to vote against any Trial of Absorption I am not sure any other Clan would help protect the Jaguars when their territory and a Invasion Corridor were the prizes.
The Invasion gutted the Jaguars exposing their logistical weakness, from '52-'59 they were a paper tiger bleeding out from a thousand cuts, and during Bulldog/Serpent what was left got hammered flat. Look what Osis was limited in being able to gather after he launched his counter of Serpent- that was all they had in the Homeworlds outside of Huntress. Bits and pieces that added up to a handful of understrength clusters only by stripping the troops from everywhere else.
If the Jaguars had survived Serpent they would have had the lifespan of a Jade Wolf.