It's not really an “idea” - thats the way just about every band in the history of rock/pop has started out. They play as many live gigs as they can, build up a large group of fans, get “noticed” by a record company and signed. Of course, nowadays the support of a record company isn't essential for modest success.
There are many, many bands, duos and solo artists why never venture inside a studio but sell live recordings at gigs and from their website.
It's not a question of “pulling it off”: it's been happening for decades. Could such a band be “successful”? It depends on how you measure “success”. If they're trying to play good music well, have people enjoy their gigs and build up fan base, of course they can. They won't be commercially or financially successful though.