DIAGNOSIS No, that's not normal. A burning plastic smell typically means something is overheating. The most common culprit is a buildup of grease and dust on the vent fan motor or the wiring nearby, which then cooks when the fan runs.
FIX You need to clean the blower wheel and housing. Unplug the microwave. Remove the grease filters. You'll likely need to take off the lower vent cover (grease duct) to get proper access. Once you can see the blower wheel, use a degreaser and a brush to clean off all the accumulated gunk from the blades and the housing around it. Check the wires leading to the motor for any signs of melted insulation.
IF THAT DIDN'T WORK If everything is clean and the smell persists, the fan motor itself might be failing and overheating internally. You can feel the motor housing (carefully, after a short run) to see if it's excessively hot. A replacement motor is the fix here.
HEADS UP Don't ignore this smell. Overheating electrical components are a fire hazard. Stop using the vent function until you've identified and fixed the problem. Running the fan to 'burn off' the smell is the wrong move.