It is possible and I know it’s happened several times over the years. If you don’t reject the schools are not allowed to offer the place to someone else.
I know a few people who have been offered places for this reason in September, after they’d started in other schools. Of course they were delighted by the offers, but they had wasted money on school uniforms etc and then had to purchase these again, for the new school.
Also if you reject on eadsmissions, the schools will still want you to confirm to them directly via email. I have 2 DD who got into very selective grammars, and even though we promptly turned down the places we were still chased by the school to confirm to them directly as well. In one DD’s case they automatically put us on waiting list for 2nd state school ( which was grammar as well) and we had to turn that down too. This was a few years ago though.
so please turn down state school offers, to make someone else’s life easier