A garbage collector doesn't need to use an algorithm like mark-and-sweep, or two space copying. It can be something as simple as a system that scans a block of memory looking for any sequence of bytes that appears to be a pointer into managed memory. You don't need special compiler support or extra program knowledge for garbage collection -- conservative collectors can be added to any language, like using the Boehm-Demers-Weiser GC with C or C++.

Automatic garbage collection doesn't even require a garbage collector -- the monolithic piece of code that performs the scanning and reclamation of objects -- it simply requires freeing the programmer from the task of managing the storage of an object. Fancy collector algorithms are meant to improve throughput and latency -- you could definitely create an implementation of Java that uses automatic reference counting but you'd be searching for something faster really quickly.

If I have a language where I create a number of managed objects and the compiler's escape analysis determines that these objects never leave the function's scope and so changes them to be an alloca then you would have garbage collection without involving a garbage collector.

Again, if that's what automatic reference counting is as sold by Apple then I'd consider it to be garbage collection.