my eldest dd went to a state nursery attached to a different primary school to the she went to. We lived between the two schools and it was easier (logistically) for her to go to the one she went to. We did try to get her into the other primary school but we were (just) out of the catchment area and she didn't get a place.
Like you, we were a bit worried about how she would settle in especially as she didn't know any other kids who would be starting school with her.
In the end we found that we were worrying about nothing - she was absolutely fine, made friends and was very happy there. No less happy than her younger sister who went to nursery with half the children she went to school with.
Hope this helps.
We may do this with dd2, who didn't get a place in the nursery at the school where ds now is because we missed the application dates because of house move. Haven't yet decided whether we will move her to ds's school for Reception or leave her where she is -- will wait to see how it pans out.
But I'm not really worried about the upheaval -- they're so little at that age that they will make new friends v. quickly, and schools tend to have lots of new children coming in at Reception anyway.
If it's the best solution for you in every other way, I'd go for it