As best as I know, most student unions, or most institutions, do issue photo ID. There might be some cases out there where they don't. But the situation you described, where it could be one piece of photo ID without an address and one piece, presumably, of correspondence, with their address while they're at school or with their permanent residence, I think would suffice.
But as you alluded to, under the current drafting of this bill, it would be up to the Chief Electoral Officer to make that distinction. I'd like to see the language a bit stronger in the bill, so that it's not left up to that Chief Electoral Officer, and it's the Government of Canada that says whether this suffices.