Until a couple of years ago I recorded an amateur dramatic groups performances using initially and elderly camcorder then a Panasonic HD camcorder. I mounted it on a tripod. The recordings were never of great quality because I had to be near the back of the audience and light levels were a major problem. Sound wasn't a problem. I ran it off mains power and in the interval changed sd card or tape. I wouldn't attempt to do it on battery only.
You have to be realistic and recognise that camcorders are not designed to work in low light levels. TV studios have bright lights and many cameras. If I was to do it again I would want more than one camcorder with an operator for each to capture the different angles and get the faces of more than one actor especially when there is a dialogue. If you have the time get a copy of the script and attend rehearsals especially the dress rehearsal.
Editing takes some time and needs a powerful PC. You may need to burn to Blu-Ray if it is a lengthy show and you want HD. But the light levels will probably mean that you will not be able to greatly differentiate between HD and standard.