Tbh I don't know how they would look into that. I know off people who have tried to start their placements later and boots haven't allowed them. Asking the manager ONCE YOU START is probably a good idea and tbh I don't see why your arrangement wont be feasible.
One reason why the manager may not be able to facillitate you is that your placement may well be to provide extra cover while regular staff are on holidays. Most staff take their holidays in July and August and are back by September when their kids are back in school.
I'd recommend talking to the manager as soon as possible but do it face to face. If I got an e-mail like that I'd say "sod him/her, plenty of others glad of work," but if it's explained they may be more sympathetic but they do have other factors to consider.
Also have your health problems cleared up? Working and studying can be stressful so be careful. Don't risk your health for a few weeks work.