If a participant is using a loan for the down payment on a principal residence, can the term exceed 5 years, or if they exceed 5 years, is the loan determined to be part of the mortgage?

Yes, it can exceed 5 years.

By part of the mortgage do you mean as an itemized deduction? To be deductible under IRS rules the plan loan would have to be secured by a mortgage obligation of the employee, e.g., a formal written document giving the plan a security interest in the residence. This not the same as a promissory note of the employee to pay off the loan. However, the loan amount could not be attributable to employee salary reduction contributions.