Nothing wrong with washing out under the deck, just so long as you follow the correct procedure.
Start by blowing down the top of the mower nad deck to remove as much grass as possible.
Hook up the hose & wash till no more crud comes out, this is important, the deck must be 100% clean underneath our you will be leaving a rust accelerating wet clod under there.
Do the above over grass engine running & blades spinning.
Remove the hose and drive over a hard dry surface, engine & blades still running and leave it there for a good 10 minutes to dry off.
The big problem is stopping the blades while there is water underneath and then the hot spindles cool down and suck the water around them inside.