Arnold GPU does indeed support Forest Pack's animation modes, Though you may find other limitations such as limited support for Max's native maps.
Another option ... really all that's happening internally is that Forest Pack is creating several versions of the object with different starting points and scattering those. You could recreate that manually for any renderer. For example, if you were to stick with Redshift, you could save out your animation to a proxy and then duplicate that proxy several times but for each one set a different start frame and then scatter those. That should give you a similar effect as using Forest's animation features.
I once wrote a proxy cloner Maxscript to automate creating those proxies. It was designed to work with V-Ray, but I've attached it in case you fancied adapting it for another renderer.