How can I drive a screw with an impact drill?
That is how it should work.  The drill is designed so that less pressure on the trigger means less power to the drill.  It could damage the driver if you were to keep it in that state of trying to turn and failing for an extremely extended period, but not if its momentary like you describe.

In short - good question but you're worrying too much. :)

Oh - yes - by the way - actually this is what it was designed for - exactly so.  It's designed to apply torque to bolts and screws and drill bits.