Bypassising is an art and a wideband oscilloscope can help. Unfortunately "Bypass" has many meanings.
The two your looking at here is to bypass RFI , either entering or leaving. The brishes generate RFI and that's where a bypass cap is useful. The power line could contain RFI and thats where a little bypassing is useful. If this was a microprocessor based unit, then an RFI filter should be fitted to the mains.
Another form is Bypassing the power supply at the IC, When the IC switches, it draws a spike from the power supply. That CAP tends to dampen that spike. At high frequencies the leads of the capacitor act as an inductor, so now you have an LC circuit which is undesirable.
So yes, a 10 uf cap parallel with a 0.1 uf Cap ceramic is a 10.01 uf Cap, but it acts very differently with frequency. The 10 uF cap can do very little with a 100 MHz signal wheres the ceramic has a chance.