My shul is extremely accessible for wheelchairs, walkers, etc. We have a ramp as well as stairs (just a couple of stairs anyway), plus two downstairs rooms for the women who cannot walk upstairs, which are directly in the back of the men’s shul, curtained off. We are very accepting of all types of people davening by us, as long as they are not disruptive. We used to have an entire group of men from a group home, who were regularly brought to daven on Shabbos by their direct care workers.
I am not certain what the halacha is regarding such a person davening for the amud (if he can in fact do so properly), but I think it is not permitted, so I am not sure about that. Doesn’t one have to be able to form a proper kavanah to be a shaliach tzibbur? In any case, I think it is a beautiful thing to see someone get an aliyah that he learned to do with much effort, as long as it is not assur.