You can but I've never felt the need for a neem drench. It's quite effective as an under-foilar spray, especially if you only have a light infestation.
Fungus gnats are annoying but if you go much lighter on the waterings, put some more fans on and keep a couple traps up, you should be able to clear your problem significantly within a week!
I get this problem quite a bit in soil grows with FoxFarm soils and a few others but seriously, it's a small issue that gets out of hand overnight and these bugs appear from thin air and also live through nuclear fallout but in the end; neem oil and azarthatin(misspelled I'm sure) work wonders for almost everything.
I guess if you feel inclined to further a humidity problem by drenching with more water, by all means...but I assure you that you will then have root rot issues. Compounding issues.