Of course that will work. Back in the day, big bands were recorded with only a few mics and very often only one. I've gotten some really great live recordings (worthy of publishing) with a stereo hand held digital recorder. It's just much easier to master and mix when you have more mics and tracks and you can isolate and augment. I try to keep that to a minimum because I really like the feeling of a live session, but that means all of the musicians have to really be in the zone to get a good recording.
There are some that will argue that the ability to isolate tracks and multitrack recordings have made musicians sloppier and they no longer play as well together live. I'm not sure about that allegation, but I can see it happening.
I will say this: I would rather have an exceptional performance captured simply than an over-processed one.
Now you all have me thinking that I need to go out and get myself another sm55. I haven't used one in almost 30 years. They were good mics as I remember.