Hello Paul,
I've found only this recommandation for the case of 802.1Q subinterface:
"Due to the way in which L2TPv3 handles 802.1q VLAN packets, the Ethernet interface must be configured in promiscuous mode to capture all traffic received on the Ethernet segment attached to the router. All frames are tunneled through the L2TP pseudowire."
see
http://www.cisco.com/en/US/docs/ios/12_3t/12_3t2/feature/guide/gtl2tpv3.html#wp1043064
In addition in Cisco Feature Navigator there is no specific voice for transporting STP Bpdus over L2TPv3.
What you suggest is possible: to verify this if you can build a setup with an external switch or you can use a cross-over cable to report the L2 vlan over a "router" port you could be able to see the STP Bpdus carried over L2TPv3.
In 802.1Q tunneling there are commands to be used to transport L2 protocols like STP, VTP and CDP but not in L2TPv3.
Hope to help
Giuseppe