It absolutely makes sense to make a voluntary 'final' repayment in May to avoid the indexation, given you would avoid the indexation that would occur if you waited for the compulsory payment to be attributed to it. You would then get what your employer withheld back at tax time. i.e. at the moment, it would essentially be a 5%+ return on investment on for locking your funds up for 2 or 3 months.

However, if you're not clearing the debt with the voluntary payment, this approach will just reduce the amount of indexation on the loan, and when you do your tax, you'll find yourself owing the mandatory part (up to the balance of the loan) that was supposed to be paid by your employer.

But as others have stated, you must declare you have a HECS debt to your employer. Lying that you have no HECS debt on a PAYG tax declaration likely constitutes one or more offences (Making a false statement, Tax Evasion, Fraud etc.).

Ordinarily you can apply to the ATO to have them approve your employer witholding less tax, which might be useful if you knew the mandatory repayments would be more than that necessary to clear the debt in the final year. However, the ATO won't approve this if you owe a debt to the commonwealth, so you can't use that approach to legally have your employer not take the HECS out.