Yes, you *could* use an 18i20 as a mixer - I used a TASCAM interface for a drum submix for some time - and it would definitely work as a personal playing solution. Plug all your mics and trigger modules into it, add a music source, plug in a pair of headphones and go. It also has 1/4 outs so you could send it to another mixer for front-of-house sound.
What will define the PA rig you use is more the size of the place you're playing, how many channels you need, and whether you're doing it for live sound (like gigs) or to rehearse. Guitar amps can also go into the PA for fully mixed front-of-house sound. Most bands can get away with a 12 to 16 channel rig, unless you're using a channel for each individual drum being miked. A couple of main speakers will suffice for a small band in a small practice space; the larger the space or the more musicians you have, look at additional speakers, larger speakers, and monitor wedges and/or in-ear channels out. There's no short answer to this, so I recommend talking with someone in person. You could always look at used gear.