Totally.

or if you have 3, add one on the snare or else a 2nd overhead depending on the room. A reverberant room maybe go with the snare (or else put that 3rd mic across the room entirely) or a really dampened room maybe use a 2nd overhead to give it some space and a kind of merry crispness

A good thing to invest in, asuming you have a soundboard, is a noise gate.
You can use it to adjust the sensitivity on your microphones, so you're snare drum's mic isn't picking up some of the kick drum in it's feed. (Or whatever it is you're micing, not just snare drums and such.) It can really be a pain when you're mixing if you have to go through channels and silence a bunch of crap between notes, because of your mics picking up noise from elsewhere. A noise gate will keep a certain microphone from picking up anything until that part of your drum is played. Unless of course, you hit something like the kick drum and the snare at the exact same time....you get the picture. That wouldn't be a problem though.

I never had much luck with noise gates on drums. There's literally so much decibel level coming from each piece that it's near impossible to not go above the threshold without setting it so high that it cuts off some of your natural decay.
Unless you're playing jazz with brushes or something, then it's not realistic.

What's a better option is that most recording software comes with mute scrub tools. Just record your drums and on each channel you can scrub a mute through all the parts where the particular drum isn't playing. It's a bit painstaking, but it allows the most control of your sound.
You end up with total isolation of all drum channels apart from whats bleeding over during an intended hit.
It's basically a manual version of a noise gate, except you control it dynamically, and after the fact.

I've had better results that way.