Is it theoretically possible that with the existing hardware in a cellular iPad model that software for the device could enable it to become a large iPhone (make phone calls + send receive texts through cellular system)? or is there a hardware limitation that would prevent this. For this question, assume a GSM carrier (i.e. T-mobile) and an iPad Air with cellular
Yes, it is theoretically possible. For example, the first iPad Air in the cellular version has the same baseband modem IC chip that the iPhone 5 has.
However please note that it is not possible for a third party app to in any way "activate" or "reconfigure" the voice capabilities through that chip. Only Apple could, theoretically, add cellular voice capability to the iPad. In my opinion, that is not likely to happen at all.
You can add voice capability to the iPad using methods other than a cellular carrier - for example via traditional VoIP or cloud services such as Skype and similar.
One aspect missing from your question: there is no iPhone?
If the plan is completely replace an iPhone with an iPad, jksoegaard is spot on.
If the idea is to supplement an iPhone with the iPad, then, with the same Apple ID in the iCloud & FaceTime settings you can have the iPad act as a secondary device. This option does not require cellular on the iPad, but does require an internet connection of some kind including cellular data. (Initial set up of the option does require a local wifi network.)
You likely thought of this, but just wanted to make sure we didn't miss something that might help.