If I take an absence that my manager has not yet approved, will my pay be reduced in some way?

No, late reporting or approving of absence requests will not reduce pay, but it is likely to delay financial reporting of the absence and the subsequent reimbursement from the central funding pool of vacation time.

Also, if you’re at your maximum vacation amount and take time off, but that absence doesn't get reported or approved, vacation accrual for that month will not be added to the total. It will appear to be forfeited. (Although this can be corrected retroactively.)