Open to correction, but I think you have to be working for at least 40 hours in the previous 5 weeks to be entitled to PH pay?
The annual leave carries forward until the employee returns.
This is from Citizens Information site
"...if you have been off work for more than 26 consecutive weeks due to illness or accident, or for more than 52 weeks due to an occupational accident and you are absent from work immediately before the public holiday because of this, you are not entitled to the public holiday."
So in this case, yep yr employee is entitled to the PH pay. Illness benefit is not means tested (so the additional pay wont make any difference) but it is taxable.