Can the thrust reversers still be activated if the landing gear won't extend?
(Source) LOT Polish Airlines Flight 16
All Boeings, minus the 717 and 727, have wing-mounted engines. A belly landing will already damage the engines and potentially rupture fuel or hydraulic lines, so no. Some reverser types employ target doors, which require clearance to the ground.
In case of tail-mounted engines, the answer will depend on the flight manual and the extent of the gear extension failure (partial, all, main, nose).
An MD-80 manual notes:

IF Nose Gear Unsafe, Both Main Gear Extended:
Idle reverse thrust may be used with caution for deceleration.