Can I wait until just before my visa expires to enroll in school?

In the interest of saving money, I’m wondering if the police/gov’t will give me any flak for waiting until just before my new visitor visa expires to enroll in a language school and get necessary papers (probably a week or so before expiration).

I have lots of history in my passport, though; even a resident visa and re-entry permits (for ARC). Will the police care about this history as long as I’m extending a new visitor visa and have required paperwork from a language school?