Doesn't sound like it was anything to do with Citrix, then, per se. The ICA sessions wouldn't have been any slower, just for being ICA sessions compared with RDP sessions, and the odbc stuff is all irrelevant to whether a session is either Citrix / ICA or TS / RDP.
Citrix as a product only talks to databases for IMA stuff. That and any other database / ODBC access is handled by the OS. Citrix plays no part in that.
All Citrix adds to TS at an OS level, is additional protocol (ICA) and requisite listener (this is ever since NT4 TSE, before that (Winframe) it was a (slightly) different OS). Doesn't make any difference to how the OS talks to databases, or the speed that it runs at. Protocol wise, ICA is still slightly favourable, although at LAN speeds the ground is close between the two.