Regarding the employer shared responsibility point made by DDelano, only paid sick leave hours must be included in hours of service. 26 CFR 54.4980H-1(a)(24) (The term hour of service means each hour for which an employee is paid, or entitled to payment, for the performance of duties for the employer; and each hour for which an employee is paid, or entitled to payment by the employer for a period of time during which no duties are performed due to vacation, holiday, illness, incapacity (including disability), layoff, jury duty, military duty or leave of absence (as defined in 29 CFR 2530.200b–2(a)). )
Here, the questioner stipulates that the sick leave is unpaid. So, these unpaid hours would not be counted to determine the employee's full-time status.
Under the lookback measurement period, it is sometimes necessary to take unpaid hours into account--but only for special unpaid leaves. Special unpaid leaves are limited to FMLA leave, USERRA leave, and jury duty. This doesn't seem to be an issue in this question.