Your HR is going to be the best contact. There’s too many unknowns. But maybe YES, in some form.

For example, my normal sick time states I can use it for me, spouse, or immediate family member. But after XX days they need more information and/or push me to apply for Paid Family or FMLA. One time? Sure. Weekly? Maybe adjust your work hours. On demand? Likely not.

Is there a reason you won’t ask HR? Or reference your handbook.