Hi Paul,
For CCM 5.1(2) yes, but for CCM 5.1(3) the Device Pack is not available. I can't tell you why this is but I just verified this again 5 minutes ago. So if you have 5.1(2) you can install the listed Device Pack to add support for the 7937 :)
Compatible Cisco Unified CallManager Release - 7937G
Note: If you have a Cisco Unified CallManager on a Release earlier than 4.1(3)SR5, do NOT install this firmware. You must first upgrade your Cisco Unified CallManager to one of the compatible releases listed
4.1(3)SR5
ciscocm.4-1-DevPack-59 or later
4.2(3)SR2
ciscocm.4-2-3-DevPack-36 or later
4.3(1)
ciscocm.4-3-1-DevPack-16 or later
5.1(2)
cmterm-devicepack5.1.2.3111-1 or later
*** (available http://www.cisco.com/cgi-bin/tablebuild.pl/callmgr-51
5.1(3)
cmterm-devicepack5.1.3.1104 or later
6.0(1)
cmterm-devicepack6.0.1.2111-1 or later
6.1
No device pack required, native support
From the Cisco Unified IP Conference Station 7937G Firmware Version 1.1(1) - ReadMe;
http://download-sj.cisco.com/cisco/voice/ip-7900ser/cmterm-7937-sccp.1-1-1-readme.htm
Hope this helps!
Rob