Short answer: Yes. An employer may require, or the employee may choose; that accrued paid leave (like PTO or sick time) run at the same time as unpaid FMLA leave, under the employer’s normal leave rules.
FMLA leave is unpaid, but the law lets employers require accrued paid leave to run concurrently with it (and employees may elect the same), subject to the employer’s usual leave policies. Running PTO alongside FMLA doesn’t extend the 12-week entitlement; it simply lets the employee receive pay during part or all of the protected leave. Group health coverage continues throughout.