I don't tune my drums.. unless something goes wildly out of tune. Or unless it's a drum that's more tone than inharmonic, like an 808 sub-kick though. Even there you often have a pitch bend going on, sooo..
I think it's mostly a thing because some EDM pretty boy producer talked about it once. I'm more of a 'if it sounds good, it's good' type of person.
As for getting individual drum sounds to gel together, you'll want to look into using bus or glue compression.
There's a whole topic of study there and about as many opinions as there are niche-sub-sub-subgenres in house music.
That won't make electronic drums sound organic though. Only a recorded real drumkit will do and recording drumkits well is an artform of it's own.
Your best bet there is to go with one of the 'live drums' softwares out there. Native Instruments has a bunch. Just saw a dude here is selling Addictive Drums, that's a popular one.