Hi Hunt,
Yes, this is a supported version combination :)
Supported versions;
Unity 4.0(5)
TSP 8.3(1)
CUCM 7.1(x), 7.0(x), 6.1(x), 6.0(x), 5.1(x), 5.0(x), 4.3(x), 4.2(x), 4.1(3), 4.1(2), 3.3(x)
Unity 4.0(4)
TSP 8.3(1)
CUCM 7.1(x), 7.0(x), 6.1(x), 6.0(x), 5.1(x), 5.0(x), 4.3(x), 4.2(x), 4.1(3), 4.1(2), 3.3(x)
Table 1 Supported Version Combinations for Cisco Unity, the Cisco Unity-CM TSP, and Cisco Unified Communications Manager
http://www.cisco.com/en/US/docs/voice_ip_comm/unity/compatibility/matrix/cutspmtx.html#wp51076
Hope this helps!
Rob