Yes and yes, although in most parts of the world it won't be legal when done via antennas. You can buy blank SIM cards from vendors like Sysmocom, which are preprogrammed but "writable" SIM cards. The important part is knowing the private key that is used to authenticate end user devices.
Then you'll just need a decent SDR and it actually works fairly well for small test setups.
Then you'll just need a decent SDR and it actually works fairly well for small test setups.