Inquire with audiomicro
and the network.
Reason is... audiomicro might give you the go ahead regardless of their agreement with the network. (which you should then keep on file) Or they could provide you with info on how to extend the license yourself, if needed, after leaving the network.
How these network deals work is the network licenses (pays for) music rights
for use on YouTube for their partners. The agreements are going to vary widely between networks and could even change in-network sometimes... which is why no-one but the network can really give you an answer. (or audiomicro, but they may be bound from discussing certain terms anyway)
Keep everything on file and follow-up with a different person if you feel unsure about an answer you get.
Hope that helps!