The idea of GSM is that carriers don't know or care what device you are using. I have used unlocked GSM phones for years and you can pop in AT&T, T Mobile or other GSM SIMS in them and they immediately work with whatever phone number and plan is associated with that SIM. If you insert a SIM with data service activated into an iPAD, it should work.
The way GSM works is that the SIM is either activated or not, so if the SIM is working in another device, when you remove it and stick it in your iPad, it should continue working on the iPad.
This is the ideal, but carriers are certainly different beasts from the ideal. AT&T for example, does track what device the SIM is in and will alter your plan based on it. Specifically with iPhone vs Smartphone data plans, because their billing system is just that bizarre. I think they may have finally stopped treating the iPhone as a special case with the shared data plans they now push.
But in general, it is safe to assume that the carriers know what device a SIM is in. They even
tell you what device it is actually in on their account management page after a few hours in the new device. The upside is that they currently don't do much based on that information other than maybe require a data plan.
CDMA is a different issue, as you can't easily switch carriers with CDMA service. However ATT, T mobile and I believe Verizon LTE only are all GSM services so you should be able to use any of these services. Not sure about Sprint. I believe the GSM vs CDMA incompatibility is why Apple has the statement on its website about "Choose your carrier at checkout because the device will only work with the carrier you choose" because you can't buy a GSM device and then later switch to a CDMA carrier (Sprint and Verizon have never allowed BYOD). Apple wants to be clear to the consumer so they simplify and tell you to go with the carrier you want instead of saying, well, yeah, depending on which carrier you initially used and which you want to switch with, you may, in some circumstances, be able to switch to some carriers (ATT, T Mob) but not others (Sprint and possibly Verizon).
The assumption here is that SIM is part of GSM, when it really isn't. You can implement GSM without using SIMs, you can implement CDMA with them. The decision to use them or not is dependent on timing, business decisions, and other factors.
LTE is indeed built up on top of the GSM branch of cellular technology, although each "generation" doesn't need to actually build on top of the last as Verizon shows. You need new transceivers for 3G vs 2G, and LTE vs 3G, so it doesn't matter a whole lot if your 2G network is CDMA and your 3G network is UTMS based
unless you are trying to share a frequency band between the two. That made sense during the 3G era as you could support both in the same band, but LTE's fundamental design is different enough that it cannot share frequency bands with 2G/3G tech. And that is why there was the big flap over getting access to frequency bands in order to roll LTE out.
As part of the LTE transition, Verizon and Sprint both moved to SIMs. So every LTE device on their network uses SIMs to authenticate with their network. They
even use the SIM to authenticate with the 2G/3G CDMA network. So the old assumption of BYOD with Verizon/Sprint no longer holds. However, there have been a lot of technical hurdles to jump still. Cellular chipsets need to be small, and there are a lot of CDMA/GSM/UMTS/HSPA/LTE bands and configurations to support. It has only been very recently that we've started seeing chipsets that are both capable of talking on all current bands with all current technologies, and they are still quite big in terms of die size. Big enough that Apple still doesn't use them in the iPhone.
Qualcomm had a couple true "World Phone" chips a couple years back, but nobody was really interested in them. AT&T/T-Mobile don't care about supporting Verizon, and Verizon only cared about international roaming. Europe is GSM-only, and China was still entering the smartphone era itself. So there just wasn't demand for them. Tablets may actually change that.