Let's see if we can get a more refined response to this question...
From an equipment standpoint, the TruTrak Gemini has the capacity to do both GPS NAV mode (via RS232 interface - does not do turn anticipation) and GPSS (via ARINC 429 interface - provides turn anticipation). If the OP's EFIS has an ARINC 429 interface module, the EFIS is capable of providing GPSS commands to the Gemini Autopilot. If the OP's EFIS does not contain the ARINC 429 interface module then the EFIS will output GPS Nav data to the Gemini Autopilot.
To be clear, the GRT Safe-Fly GPS is a position sensor. It provides position and rate data ONLY. It needs another box (like the EFIS) to do the actual computational work of navigation. That other box has to have a database of waypoints (NAV Database) to use in these computations.
In short, the Safe-Fly only knows the current "I am HERE" position and the "I sense I am moving in that direction" velocity information. The EFIS gets this "I am HERE" information and, through pilot input, is told "I want to go THERE". The EFIS does all the calculations necessary to provide a steering solution to get from HERE to THERE - that's how we get the magic magenta line.
The EFIS then spits this navigation solution out its digital interfaces to the Gemini autopilot which, in turn, drives the airplane down the magenta line.
1) VFR Use: The combination of the GRT EFIS NAV database and the Safe-Fly position data will allow a pilot to conduct autopilot-controlled flight from waypoint to waypoint. Depending on whether or not an ARINC 429 interface module is present, this navigation may take place with or without turn anticipation. With ARINC 429 interface the autopilot will also provide vertical guidance.
2) IFR Use: In this case, the situation is very much as noted for VFR, except that one needs to have new enough hardware to run the GRT IFR software, and one needs to pay to have that functionality enabled. One also needs to have all the necessary IFR databases loaded. In this situation the combination of Safe-Fly GPS and EFIS are acting like a GPS navigator (GNS, GTN, IFD navigator). This mode of operation should also enable the aircraft to fly coupled approaches if an ARINC 429 interface is available from the EFIS.
I won't comment on the legality or advisability of using the EFIS/Safe-Fly/IFR Database combination in IFR flight - that's up to the aircraft owner/operator to make that call.