Generally, no. Sick pay is usually reserved for short, health-related absences, for example a cold or flu, staying home to care for a child who's normally in school, or recovering from minor outpatient or dental procedures. Paid Family Leave, on the other hand, relates to a paid absence from work for an extended period of time, for a qualifying reason.
However, third-party sick pay differs from regular sick pay in that it is paid by somebody other than the employer (usually an insurance company that specializes in this kind of coverage for employers). Because third-party sick pay is almost always used for absences of a longer duration, it generally fits the definition of paid family leave.