Yes, If you get the apk file somehow.
Some ways to get apps from the play store without installing google apps & services are described here:
Sure, there are always some apps that won’t work on some devices.
Some won’t work for software reasons (e.g. need Android 6+), some for hardware reasons (e.g. need NFC) and some for no apparent reason.
Oh, and don’t disable privacy impact, or many apps that do work will misbehave.