Digi Mesh is a proprietary mesh network created by Dig. It is designed to run on Digi’s XBee modules which do not use a TI chip set. But there are Raspberry Pi shields that you can use the Digi Xbee modules on which will allows you to use Digi’s mesh capabilities.
IF you are referring to if Digi’s XBee ZB modules are capable of communicating with a TI Zigbee chip set, then the answer would be yes. Providing that you set the ZS parameter on the XBee accordingly and that your TI chip uses a Zigbee PRO certified stack and the Public profile.
As for the Raspberry Pi, there are 3rd party adapter boards and sample code available for communicating with the XBee modules.