AFAIK, no OS uses a "GC-like mechanism" to handle page allocation.
When a process requests additional pages be added to its address space, they remain in that address space until the process explicitly releases them or the process exits. At that time they go back on the free list to be re-used.
GC implies "finding" unused stuff among something other than a free list.
I was mainly thinking of the zeroing strategy: when a page is freed from one process, it generally has to be zeroed before being handed to another process. It looks like Linux does this as lazily as possible, but some of the BSDs allegedly use idle cycles to zero pages. So I'd consider that a form of GC to reclaim dirty pages, though I'll concede that it isn't as common as I thought.
When a process requests additional pages be added to its address space, they remain in that address space until the process explicitly releases them or the process exits. At that time they go back on the free list to be re-used.
GC implies "finding" unused stuff among something other than a free list.