There is already two transistor (probably fets) inside the atmega to switch the output pins high low.
So yeah, a transistor will work perfectly fine at passing the PWM signal. PWM is pretty slow compared to what a transistor can handle. eg, 1,000Hz PWM and the transistor can switch at 100,000,000Hz
All you need to do is make sure the current you feed into the base is high enough to turn the transistor fully on given your load current.
Simply put, if the transistor has a gain of 100 and your load draws 1A then you need to put more than 1A/100 = 0.01A (10mA) into the base. So you might pick a base resistor that puts 20mA in for example.