Hi,
With TMR3 configured as a counter I would think you should 'get' the count. However the datasheet isn't really clear on this as far as I can see. It does say that, when entering sleep, all peripherals are shut down so perhaps it'll stop working even if configured as a counter. If configured as a timer it'll definitely stop since the main oscillator is shut down when in sleep.

If it turns out that TMR3 stops counting when in sleep you could try OSCON.7 = 1 which, when the SLEEP instruction is executed puts the processor in Idle mode instead of sleep. In idle mode the CPU is shut down but the peripherals are kept ON. Draws a bit more current obviously but what are going to do.... Make sure you read up on the various idle-modes available. But again, I think you should be fine when configured as a counter.

/Henrik.