I agree with Pilesar, a "simple" flash calculation should provide most of the information needed (even if it doesn't fully answer the question of whether or not the system is fully at equilibrium).
Focusing on the main claim (nearly all of the C2/C3/lightest components will pass through the vessel), the one thing I see missing from the problem description is "quality" -- how much of the feed stream is actually condensed in the vessel. For example, if I see that I'm feeding 100 SCCM of gas to the vessel, and the vapor stream to the GC is flowing at 95 SCCM, That suggests that only 5% of the feed is being retained, and, since C2/C3 will strongly prefer the vapor phase, I'm probably justified in saying that nearly all of the C2/C3 in the feed stream is ending up in the vapor stream. The flash calculation should allow you put an estimate to what "nearly all" means.
Alternatively, I could have 100 SCCM feed rate, but only 20 SCCM in the vapor stream. That would suggest 80% of the feed is condensing, and it will be difficult to say that "nearly all" of the C2/C3 is coming out in the vapor stream. Again, a flash calculation should allow me to put a number to that claim.
Even if you end up deciding to explore the possibility that the vessel contents are not fully equilibrated, an equilibrium flash calculation should allow you to begin evaluating any claims about how much of what components are passing through the vessel and which components are being held up in the vessel.