No. Employees can’t apply for paid sick leave if they fall sick during no-pay leave or any other non-working day, e.g. public holiday or annual leave.
Example:
Company implements 1 day no-pay leave per week.
Employee agrees to take no-pay leave on all Mondays.
If the employee is unfit to work for both Monday and Tuesday, he or she is only entitled to 1 day of paid sick leave, i.e. for Tuesday.
As your employee agreed to cost-saving measures to support your company, as an employer, you are encouraged to exercise compassion and reimburse any medical consultation fees.