Is it possible that a multi-rotor polycopter of some kind could escape Mars' atmosphere from its own propulsion?
Reaching orbit using aerodynamic lift from a rotor like an Earth-based drone is likely impossible. The atmosphere on Mars is very thin compared to Earth (by about a factor of 100!) so lift is much harder to achieve. At best, you'd be able to do short hops, but nowhere near orbital speed.
That said, a powerful enough launch vehicle could be equipped on a lander for a sample return mission. However, it would have to use conventional rocket engines to have enough thrust.
The launch vehicle for sample return would need about 4.1 km/s of delta V to reach orbit from the Martian surface. It's possible it would then perform a rendezvous with another transfer vehicle, which would occur once in orbit for the retrieval capsule.
Related question with more information: Could a helicopter fly on Mars?
Check out this video for helicopter-like test in a simulated Martian atmosphere: