I would say yes and No! This would only be limited to the phone processing a change to the internal memory, a log somewhere recording deleting and installing a app - but marginal data, couple of KB etc.
Smartphones always feel quicker when new, or after a complete wipe and reinstall.
No this shouldn't have any impact on your phones speed. Obviously the less apps you have filling up your storage the quicker your phone would be. Bu this shouldn't have an impact on the speed.