That is a hit or miss kind of thing. You will have to experiment.
In microG Settings make sure ‘Google device registration’ is on. ‘Cloud Messaging’ too I suppose. After making certain changes in microG a reboot is recommended.
Usually a good idea to have GCM enabled before installing apps that need it. Otherwise they may not register for push notifications.
Add account via Settings → Accounts (icon with white G on blue square) or within microG Settings.
Or see this thread…
Any way to use “Login with Google”? - Using /e/OS - /e/OS community