I don't think it works that way...?
@KRowland
Is an ASCAP license all I need to use music lawfully on my website or digital service?
An ASCAP New Media license does not authorize the public performance of the repertories of other U.S. performing rights societies (such as SESAC or BMI or GMR). Nor does it authorize the reproduction and/or distribution of musical works; and/or the performance, reproduction and/or distribution of sound recordings. Each of these uses requires separate authorizations from the respective copyright owners or licensing representative. For example, to obtain a mechanical or synchronization license for the reproduction and/or distribution of musical compositions (PODCAST DOWNLOADS), please contact the appropriate music publishers and/or the Harry Fox Agency. To obtain authorization to perform or reproduce sound recordings (INTERNET STREAMING), please contact SoundExchange or the record company associated with each particular recording.
https://www.ascap.com/help/ascap-licensing