Yes task force training is seperate from crew grade, and both are associated to individual ships and are unaffected by the absence of the task group HQ.
Crew grade represents the crews ability to perform tasks, better hit chances with beam weapons, shorter jump blindness, etc. Task force training represents their ability to carry out orders in a timely fashion, low training leads to things like missiles being fired off by individual ships at different times instead of the task group firing as one, slow reaction to change target/destination, etc.
There is no need for ships to be in the same system as their task group HQ, though they only recieve the various bonuses listed on the HQ screen if they are in the same system.
