I suppose the up and down motion tends to "shake" some grass loose and is probably a good idea.
A mower will sure but better if you keep the buildup underneath clean, and mowing wet grass will clump up everywhere.
The deck needs that air flow to suck the grass up and whack it off level.
If you want to get serious about cleaning underneath, get you one of these.
Mower Lifts Hand Trucks Lawn Mower Jacks - MoJack-The MoJack