Yes, you can always receive a call on Silent Phone, no matter what you may be doing on your device. If your phone is on and Silent Phone is active and running in the background, it will ring when someone calls you, even if Silent Phone is not active on your screen.
Once activated on your device, there is never a need to log into Silent Phone. On mobile devices, Silent Phone utilizes “Push Notifications” and “Background Data” functions to operate. If you are unsure if these are enabled on your Apple or Android device, check your device’s settings.