I hear your concerns Seansmom, and I've been right where you are. Based on my experience in the past two years, the simple answers to your questions are "yes". SPD can cause toileting problems due to poor interoceptive sense, and diet can cause toileting problems as well. I only learned about the latter in past three months. My daughter (5 and a half) was not and is not totally potty trained. However, we discovered after purchasing the Feingold diet program and keeping a food diary, that she wet her pants every time she ate something with citric or ascorbic acid. It took some time to figure this out, but eventually we eliminated citric/ascorbic acid from her diet, and it cut her wetting her pants from several times a day to 4 or 5 times a week, and then only slightly wetting, not fully letting go. A couple weeks ago we discovered she also has a corn sensitivity, and now we're working on eliminating corn derivatives (they're everywhere--even worse than citric/ascorbic acid) and expect that will finally eliminate the wetting. We intermittently have problems with her soiling her pants and are investigating a benzoate sensitivity. I haven't been able to figure out how benzoates cause her to poop her pants, but when she eats a food high in benzoates, she poops her pants within an hour.
The thing about poor interoceptive sense is that when she does have an accident, she doesn't even seem to notice. She'll sit in wet or soiled pants for hours if no one notices and not seem the least bit uncomfortable. We've tried two therapies that are supposed to help with this sense, but not much has changed outside of the diet changes. We've done the Wilbarger Brushing Protocol and Therapeutic Listening. I don't think they hurt, but neither did they help.
I've done so much internet research, it would take a much longer post to give you all the links regarding the sensitivities mentioned above, but if you Google citric acid sensitivity and benzoate sensitivity you can follow the links to gather a lot of information.
Feel free to private message me if you need support or encouragement.