Access to Virtual server and pool configuration question, thanks!

Yes, using a standard virtual server configuration, you'd need a separate VS for the UDP traffic. Can you use client source address for persistence? If so, you could create a source address persistence profile and set the "Match across virtual servers" option. Otherwise you'd some other pervasive value in both TCP and UDP requests to persist the traffic.

Alternatively, depending on what you're trying to do at the proxy layer, a performance layer 4 VIP may also be an option as it supports an "* All Protocol" type.