Health wise it should do no harm. But like Chris says, you'll end up with some hodge-podge of breed/colour so you can't claim them to be pure something if you want to sell them. If they were brilliant layers, somebody might take them for eggs but I guess they're not? And they're not going to be good meat birds. So your only market for the chicks is somebody who just wants some pet chickens around and doesn't care what breed they are, nor how much they lay. So you won't get much money (if any) for them and you may be pushed to shift them. Clearly if you're prepared to keep them yourselves, go for it! You may end up with some beautiful chickens but just make sure you've thought it through so you don't end up with a lot of chickens that you can't house and can't be sold.
If you want to hatch something, why don't you buy a few hatching eggs in of a purebreed? I've got a dodgy cockerel having lost my two pure breed cockerels so I've bought in hatching eggs this season in the hope of getting some decent breeding stock for next season.
H