I've found Japanese carriers to be particularly troublesome when it comes to using your own devices, but I haven't tried in a while.
If you are able to buy a sim card and data plan for a smart phone, there's no reason you couldn't put that in your tablet, as long as it's compatible with the carrier. I just haven't yet found that option when I've visited. I once put a softbank sim card into my iphone and it worked just fine, but the bill was ridiculous, despite hardly using data at all; I think it was because we didn't have a data plan for the sim card, and not because the iphone wasn't from softbank.