I’ve never heard it used as a greeting, and I would think it sounded goofy if I ever did. “Welcome Inn” is just a friendly name for a motel, not necessarily a pun. There is also a “Welcome Inn Social Services and Community Centre”.
Could it be a contraction of “welcome, come in!”?
In Twin Cities, I’ve never heard it said as such. Usually, it’s “Welcome! Can we help you find something?” Or “Welcome, let us know if you’d like help with something.” Grammar is a bit of a thing with a lot of people here.
“Welcome in!”
“Welcome out!” (pushes toothy greeter out the sliding doors, locking them.)
I’ve heard LGBTQ people say “Welcome out”, but that’s something else entirely.