An 18V cordless drill is probably overkill for installing drywall, but
it would certainly work. Several years ago, I remodeled three rooms in
my house and used a 9.6V Makita drill (6095D) to install the drywall.
I don't know what the current rating is for the motor as it's not
listed on the drill or in the manual. Anyway, it did just fine driving
1-1/4" screws, but I do admit that I own and used two batteries for
it. Each battery lasted longer than the 1 hour recharge time, so there
was no waiting for fresh battery.

I didn't even bother with a drywall clutch attachment. I started out
trying to use the 5-position clutch on the drill, but each stud or
ceiling joist seemed to have different densities, so that didn't work
very well. I ended up setting the Phillips bit almost all the way into
the Jacobs keyless chuck and set the clutch to the drill position.
This resulted in the screws going just far enough into the drywall to
be 'below' the surface without breaking the paper.

Generally, B&D tools tend to be 'handy homeowner' disposables. That's
not necessarily a bad thing because they are relatively inexpensive. I
would just pitch it and buy another brand new one for $30 or so if I
wanted a corded drill.

Regarding Harbor Freight electric tools, I also consider them to be
disposables. I bought a Chicago Electric reciprocating saw from them
for $20 so I would have one that I could beat to death and not worry
about punishing my nicer one.