You'll definitely be allowed. Well, they can't not allow you. It's your choice. They can advise against it if you have any serious complications, but they can't tell you that you can't have one. You're the only one who can make that choice. I can't see why they wouldn't recommend it though, as SPD might be miserable for you some days, but it has no impact on your baby's health (or yours either for that matter, other than the pain). And actually, you're more likely to be able to stay relaxed and in a position that doesn't involve being on your back if you're at home, so that should actually help to minimize any discomfort you have from the SPD.
I have some mild SPD. It's manageable though and only started at the beginning of 3rd tri, and no one's even raised it as an issue in relation to my planned home birth. Btw, give yoga and osteopathy a try for the SPD. I'm prone to SPD anyway because of some issues with my joints, especially in my lower back and pelvis, and my connective tissues, but yoga helped to keep it away until about 28 weeks. And since then seeing an osteopath every few weeks has helped tremendously. Some days I don't feel any pain at all and even on my worst days, it's much, much better than it was before I started treatment. You have to pay privately unless you can get a referral from your GP (you might, so it's worth a try), but it's definitely worth it.