In Crysis on 1920x1080, everything on Very High and 16x AA I get pop up on vegetation and objects that are far off in the distance. However, I would like to try and remove pop up completely if possible. It's just kind of lame to see a rock or tree appear suddenly, even if it is far away.
I am running i7 2600k at 4.5 ghz, gtx 560 sli, gskill 1600mhz 9-9-9-24
To be honest, I don't think you can help that. If you have everything Maxed and the AF at x16 then thats as much as you can do. unless you can change something in the .INI file and make it so the view distance or something is bigger so you no longer see "Pop up" anymore
You have to change a .ini file to achieve this to expand the view distance further, this will though drastically reduce performance since this will affect everything that renders in the game, not just vegetation.
Your video cards ( GTX 560 Ti ) and that too at SLI, is really good. You don't have to upgrade it, or at least not now.
As everyone else said, you have to change a ini file, that is in the CVAR groups.
And as for your question, no, your problem won't be resolved if you had better GPUs. That is , unless you have changed the view distance, then performance won't be affected.( at least not much FPS drops )