Need to preface this with i have never used a battery welder. Think i would work BUT, you will have no current control. Tig and stick welding use constant current power sources, when you stick weld the current is stable and the voltage varies. Mig welding uses constant voltage power sources, the voltage is stable and the current varies. So the mig welder previously posted would be a good choice for using batteries. Might be willing to try it in an emergency but it is not something i would want to stick weld with for any length of time. Of course i tend not to do much stick welding anyway, i can tig weld in air conditioned shops with out fuming up the place.
Something else to mention, batteries produce hydrogen gas. Keep the batteries away from the welding area, or at least where the spatter is not going to land on them. Some of this has already been mentioned, no exposed skin unless you want a 3rd degree sunburn. Cotton, wool, and leather will only burn, synthetics will melt to your skin while burning. And you will get burned. If you are welding overhead use earplugs, aside from all of the other protective clothing, welding spatter going ZZZZZZZZZZZZ round and round in your ear canal is nowhere near as much fun as it sounds.
Use the correct eye protection. Gas welding uses a shade 5 lenses, these are really dark sunglasses. When electric welding, use at least a shade 10. The shades go up to 14, with a shade 14 you can stare at the sun with out harming your eyes. The higher the amperage you use the higher the shade you need. The auto dark helmets are really nice, especially if you are learning to weld, you can see what you are doing before and after you strike your arc. If you buy one make sure that it has IR and UV protection even when it is in it's light state (about a shade 4 for most i have seen). That way your eyes are protected if it goes light while you are welding. The down side is the auto darks tend to be heavy, more of a problem if you are wearing on a daily basis. And they are more quite a bit more expensive than a regular welding hood. I have a variable shade, variable sensitivity auto dark hood that set the boss back around $300. Remember thinking that this is cool, and then he handed me a production welding job that lasted over two weeks.
Blast, taking a welding class is a great thing to do. That is how i learned to weld. And while i don't normally do welding for a living i wound up with a temp job working at a testing lab for a while as a welder and one of the fixtures i fabricated out of aluminum was subjected several shock loads over 250 g's and the fixture stayed together. BTW the fixture weighed over 200lbs. As far as convincing your DW point out the things around the house that welding will fix, and you can take those things to class and burn big holes in them.