Yes. Unless you are on social assistance or in bankruptcy. Income is typically only considered when the primary applicant has accompanying dependent with a child. (ie wife comes with accompanying adult child that has a child of their own (ie grandchild or PA).
Not to overly complicate this, but I'd say income is only
formally considered (i.e. with submission of the financial forms) in that specific circumstance that you mention.
But spousal cases - income -
is considered - a sponsor is expected to be able to support the spouse. They just don't set minimum incomes.
What you're absolutely correct about is that they don't set a minimum amount - so as long as the sponsor is basically working (or some other form of income), shouldn't be an issue. It's also perfectly fine (as far as I can understand) to show/mention that the spouse will also be working and/or capable of supporting him/herself. Repeat, there's no minimum income requirement.
Anyway: all that a long way of saying, yes, a student who works part-time should be fine, as long as some ability to support self and spouse. IRCC will probably not inquire or ask for more info unless the situation has some clear problem with capacity to support (eg no income or place to live).