Direct answer: Yes. Eagle’s 1000/2000 manual says Eagle gate operators work with all brands of receivers and provides a pre-wired terminal for a 3-wire or 4-wire receiver.
What that does not mean
It does not mean every remote will still work. Once a different receiver is installed, remote compatibility follows that receiver. Check receiver voltage, wiring, and the receiver manufacturer’s instructions.
Source checked: Eagle 1000/2000 installation manual