I'm under the belief that no iPad is carrier locked. You just pop in a valid SIM and it'll work. However, some carriers have locked a newly activated SIM to a specific device, that's a different story.
My 200MB "free data for life" T-Mobile iPad SIMs were not transferrable between iPads the last couple of times I upgraded hardware. I was forced to acquire a new SIM to activate the service on a new device.
What do you mean by "old T-Mobile promo SIMs"? Unactivated SIMs don't have any special features built in, those are added to the account after the SIM is activated; it's just a dumb identification chip.
If you are trying to get the 200MB/month "Free Data For Life" tablet service well you are out of luck since T-Mobile US stopped those activations about a month or two ago. Even if you acquired a SIM earlier for said free service, T-Mobile will no longer accept any new activations.
iPads with previous activated "free data for life" SIMs continue to function beyond this new signup cutoff date.