One of my branch sites far out of town experiences primary link failure from time to time which is very disruptive. All they have in terms of connectivity is a T1 for data and PRI for voice. Would it be possible for me to configure a backup link for data (not voice) traffic using my Callmanager's PRI?
If you're not using all your bearer channels for voice, you can provision some of them for data. Practically speaking, you would need to use at least half (12 channels).
I am assuming that if the office is small enough that a data T1 is sufficient, you don't need very many bearer channels for voice. The channels have to be one or the other. I suppose if it's a call center or something similar, that assumption doesn't hold.
Dial backup is (almost) always an option, either to a dailup ISP or direct to one of your other sites. This depends on the capability of your router(s) and PBX(s).
The simplest is an external analog modem connected to one of the router's serial ports. (commonly done on a Cisco AUX port, but there are limitations there.)
A more complex, and expensive option -- if your PBX can do it -- is an ISDN BRI. That can be directly to the router, or again, through an external "modem" (TA).
It's called Integrated Services for Multiple Call Types. This IOS feature is 10 years old or so.
ISDN interfaces can support both data calls and voice calls. Typically, this is done using one interface for data and another for voice. This feature enables data (dial-in, dial-on-demand routing [DDR], and DDR backup) and voice call traffic to occur simultaneously from the supported ISDN PRI interfaces. To enable integrated services, the interface used for incoming voice calls is configured to accept multiple voice call types.