If the employee can show any signs of undue pressure by the employer to terminate or vary the contract throughout the performance improvement process (admittedly Personal Sickness / Stress), they can raise a constructive dismissal case.
It may not be a strong case, but the risk is still there.
For what its worth, I would deal with this case by acknowleding the resignation letter, however not accepting it until the employee returns from Personal Leave and has a constructive conversation with
HR / Management explaining the reasons.
It is irrelevant whether they accept or decline the offer, but you have taken all steps to resolve the matter.