Yes I guess that is one way of going about it but.....No it is not necessary to "drop the entire deck and flip it over" to gain access to the under side of it. You would need to raise the entire mower to gain access to the under side of the deck.....that is "IF" you are willing to do so...if not then don't know what else to tell you.
Get yourself something like this maybe?
I have had a few this year that had to use the air chisel to break through the built up grass under the deck. Twisted knot wire brush trying to clean the buildup off the blades prior to sharpening just polishes it to a nice gloss finish.
That is basically what I have had to do under my mower deck.
I have a Hustler Raptor Flip-Up that can flip up the entire deck to gain access to the under side of it to change blades, clean the under side of the deck, etc......believe me it makes life a bit easier.
I gave up on trying to prevent build up of grass, dirt, etc. from accumulating under the deck after each time that I mow the lawn (which is a little over an acre).
Since then, that is, after I am totally finished cutting the lawn I move the mower to a flat concrete spot, flip up the deck and.....you bet.....there are clots of a combination of grass and dirt all under the entire deck!
So what I have been doing is using a metal chisel and wire brushes to clean the entire underside of the mowers deck. Yes the process is a PITA having to do this each and every time after every mow but it has to get down.
You NEVER want to leave any clogged dirt and grass, etc. under the deck because once you do...over a period of time it hardens up and it really becomes difficult and hard to remove.
Just my $0.02......to each their own.