Yes, but to be clear, it still depends on the quality of their meditative concentration.
An advanced meditator who is honoring their path of dedication or devotion will be desiring and concentrating on truth (on who they truly are) to a relatively high degree, even though all beings are doing their best to advance in their paths within their perceived capacities. The ability to effortlessly maintain this concentration will also be increasing in more Self-realized states, because for the Self, the ultimate Creator, effortlessness is a natural state.
When concentration deepens on truth, on who we truly are, less automatically arising thoughts are experienced in the mind, because thoughts are an auto-pilot function of the mind which is not united experientially with consciousness deep enough. (Thoughts can also be consciously used as a tool for communication.)
If an advanced meditator stops honoring their path, the greater energy they have access to will start empowering their not completely purified mental tendencies, and because of the greater energy, greater and more powerful thought activity will be experienced. This might be unpleasant, and a state of suffering, yet even in this, there are lessons of learning.
In all cases, all of our experiences are moving us forward in our learning. The one who doesn’t honor their path will temporarily arrive at a different destination than their enlightenment, will have the chance to see their mistakes, will need to work through the subconscious energies they have accumulated, and ultimately, all of this will accumulate in greater wisdom and they will be able to realize the truth of their being.
When we sincerely desire to experience and concentrate as best as we can on our Self, we keep evolving in greater acceleration towards a mastered mind where presence is greatly fulfilling the need automatic thoughts are trying to fulfill when there is lack of presence in the mind/emotions/body.
When we are more in the mind/emotions/body, when there is presence/we are present in a greater degree, there are less automatically arising thoughts.