When Android enters sleep mode, almost everything is shut off. Only basic system apps and GSM/CDMA radios are left on to receive texts, calls, push notifications etc. Services, Activities are all shut off, and the CPU is put into a low power mode. Depending on what the user chose in the wifi settings, the wifi connection may or may not switch to mobile data or shut off completely.
If you want to keep processing, but don't need the screen on to interact with the user, you should acquire a PARTIAL_WAKE_LOCK in which the screen and keyboard are off, but the CPU is kept on. However, remember to release the wake lock when you are done, as PARTIAL_WAKE_LOCK
is the only one of the four wake locks in which the CPU will continue to run until you release it or your app is killed. Forgetting to release the wake lock can be a huge drain on the user's battery.