Industrial heat applications have studied evaporative rates under every conceivable condition - you don't need a prototype to know that 1m3 of air travelling through a few dozen yards of wet, vertically-strung yarn will evaporate enough to bring that 1m3 of air to saturation. It's not an engineering 'if' - the barrier to people *looking* at such an idea has been the fact that the moisture flies away and rains in a large area, so you cannot easily make a *business* from it.
Global warming does increase total evaporation, yet it only increases that evaporation in the places that *already* get *too much* water - hence, floods. At the same time, global warming increases the Hadley and Ferrel cell circulations, and those drive a dry down-draft in other regions (the 'Horse Latitutdes') which makes those alread-dry regions even drier than normal. That's how global warming increases floods *and* droughts; it's adding more water to the spot that already had plenty.
My design specifically does NOT do that - we would be adding a little water back to region which only *recently* began to dry-out, such that they return to the natural state they were in, *before* climate change. Water vapor does not 'linger' for weeks, accumulating, from an evaporator - it moves across the land, instead, depositing a small amount of rain. That evaporation *only* takes place during those HOT and DRY periods when rain is needed, and no flash flood is possible.
A flash flood, specifically, comes from miles and miles of an 'Atmospheric River' that carries immense amounts of water, ploughing-into a cold front, which causes all that water to drop at once. The cold of the Himalayans, striking the warm, humid waters of the South Pacific, are what cause floods in South China, for example. This is NOT some mystery doomed to destroy us; we already accurately predict hurricanes weeks in advance, without *failing* to predict a hurricane, when one did occur. Our weather models have NOT *missed* catastrophes - they keep spotting problems before everyone else. So, no, we won't be blindsided by sudden flash floods.