No, the trigger has no bearing on it. But the revolver is more likely to light strike when fired double action as opposed to cocking the hammer single action.
If I had that revolver with that issue, I figure there are three ways to go.
1) Call Taurus. The experience of most people is that sending it back will ne expensive and also take an irrational length of time.
2) Visit the Wolff gun spring website and order a new hammer spring. Does not cost a lot and shipping is cheap also.
3) Attempt to shim the spring that is in there now in order to get a little more energy out of it.
Me? #1 is almost completely out of the question. I would do #2 first and then do #3 while waiting for the Wolff spring to arrive.