A properly setup mulching kit, installed on good equipment, does not put any extra stress on the engine. I should add that the operator must maintain and keep it clean.
Sorry Rivets, but the Magic Pudding was a fairy story.
If you are asking the mower to recirculte & recut the clippings then all that extra air pumping does put a substantially bigger load on the engine.
Weather you notice it or not depends upon just how much the mower was overpowered in the first place.
So top end mowers will not have much effect as most are powered at + 30% or better of the design load
Engine companies usually recommend mower companies fit an engine + 20% over the dsigned maximum load.
Store brand specials are generally at or marginally above design loads.
you are however spot on about proper maintenance reducing the extra power draw and sharp blades are no 1 on the list.
And as for wet grass should be a no brainer.
It is one thing that always amazes me when I go to fit new blades to customers mower and they tell me not to fit the same one because they did not , cut / bag / mulch properly.
When I get under the deck there is generally no edge left on the blade let alone a sharp one and the entire cutting zone is worn back to a nice round club.
I have given up arguing with them and just fit some Stens Gaitor type blades and wait for them to come back with a cracked & fractured deck because big lumps have broken off the blades but they won't change them because "it still cuts the grass"