Hi!
A few points. The Stark title in the Q store is actually called a core, technically, though I suppose you are correct (all cores are modules but not all modules are cores I think).
Second, should you just play your custom or both your custom Stark and the main store title Stark. That depends on you.
For example, for me in your situation, if I created a custom with Stark as the sole core, then I would probably have no desire to play the other.
If, however, there were say 4 cores, the others of which are just as dense if not more so than Stark, I might consider it. But that’s a big might.
To answer you shortly, no. I personally wouldn’t bother. Stick to your custom.
For whatever reason, I always forget the exact answer to this question though I know it. I think it does something along the lines of, the modules within the core (Stark) are there to support the function of the core within your subliminal, it doesn’t contribute to the custom as a whole. That’s what the actual modules (Gloryseeker, Spotlight, Dominion…) are for.
Hope this helps.