Provided that you are honest, I don't see any ethical problem with what you propose.
Sure there are some deeply company-centric views of the world that would say as soon as a company does you the immense favour of permitting you to do work for them, paid or not, then it is your primary moral duty to obey them in every respect, never to question or negotiate their terms, to protect their interests at all times, and show them grovelling gratitude, until such time as they cast you aside or you quit. I exaggerate this POV, but in the worst cases only slightly. You don't owe them all that, so figure out what duty you you really do owe them, and if you change your mind as to whether you want to fulfil that duty, tell them.
Honesty means not lying about when you arrived, and it also means not concealing that you're in breach of any agreement you might have made with them as to when you will arrive. If you're doing neither of those things, you're not cheating them out of anything.
As everyone else has said, it might not be to your maximum personal benefit to be unpunctual, for a variety of different reasons. But it's only unpunctual if you're later than you're supposed to be. You are entitled to ask for or offer different terms (including start time) from what they're initially expecting. You have no ethical obligation to wring every single moment of time on-site out of this internship, neither for that matter do you have an ethical obligation to get the best possible reference from your mock-employer at the end of it.
Regardless of whether or not you're getting anything of value out of this internship, you have an assignment as part of your studies. Unless you get explicit agreement otherwise, part of the assignment is to follow the routine of a genuine employee, which usually means turn up on time. You're free to complete your assignment in full, or not, and your decision has more consequences for you than anyone else. They probably won't fire you for repeatedly being up to 15 minutes late, and almost certainly not without a warning, so if you're happy to give the impression of being a little lazy and/or disorganised and/or disrespectful, then I suppose it's all part of the learning process to find out what (if anything) happens to people like that in this particular workplace ;-)
If there's some specific reason why starting at 9.15 is better for you than starting at 9.00, then the smart thing to do is probably to discuss this with your boss at the company. Some people will be quite flexible, especially given they aren't paying you, and even more so if they're getting valuable work out of you for little supervision. Others won't be flexible, but at least you'll know the score. On the other hand, if you just want to be "15 minutes late", no matter what time you're supposed to be there, as a protest against the fact you're being used for unpaid labour, then I would suggest it's smarter just to get over it, and accept the terms under which your degree is awarded despite not liking them.
In some industries, it's a simple fact (at least in the US and a handful of other countries) that unpaid internships are the payment you're expected to make up front, in order to get a real job in the industry later. It's not unethical for you to offer them less than full payment, that's called "haggling", it's just less likely to be accepted. Even if you never want to work in the industry, and therefore don't care about the experience or the reference, if it's required to graduate then it's likewise part of the payment you make for your degree.