Sorry if I am wrong. Is resin hydrophobic somehow and ionic liquid is completely composed of ions? I don't expect ionic liquid to be adsorbed by resin...
The question is what has a higher binding affinity to your resin- the IL, the solvent or the sorbate. If you have some IL in the resin and the resin has a higher affinity for the sorbate, it will displace the LL from the resin, and will then float free.
So yes, it depend on the IL, the resin, the solvent and what you are trying to absorb.
No surprise, when you impregnate polymeric microporous particles with IL and both have density below one they should float on surface. But, this makes no problem, even at moderate mixing in batch operation particles are well distributed in liquid. It is better to speak on extraction into impregnated extractant (IL) instead of adsorption when IL is responsible for separation. You can look to our paper in React. Funct. Polym., 71 (2011) 736-744. We used such particles in packed column without problem.