The "spraying" part of the job isn't particularly messy or smelly. As noted above, some of the powder will end up on the floor but easy to broom or vacuum up. So I don't think there's any problem doing that part in your basement.
The baking, on the other hand DOES have an obtrusive odor. I don't know that it is particularly harmful but I can imagine it would linger in the basement and get into the rest of the house with ease. Not something the wife and family is likely to be pleased with.
If at all possible, I would recommend installing your oven in the garage and doing everything out there. Just a lot less hassle.