The Time Tracker runs independent of the Gemini Desktop. The Time Tracker requires all time connectivity to your Gemini, so your PC/laptop should have Internet connectivity.

This said, the answer to your question is yes, you can user Gemini Time Tracker while using Gemini Desktop in offline mode, provided you have Internet connectivity (to your Gemini). One word of caution, your work in Gemini Desktop offline mode will not be visible in Time Tracker until you synchronize Gemini Desktop with your Gemini.