Yes. 

However, it is good to keep in mind that some religious practices that are very emotional, crowded, or energetic (such as visiting the holy sites on Arbaeen) which are fine for most people may be overstimulating and trigger mental health episodes in someone vulnerable, even if one hopes for blessings and healing through them at the same time, and they can also bring healing. Also, sometimes, mental health conditions are masked as excessive religiosity and piety which are then inadvertently encouraged by people around them.
So it is good to be thoughtful about what is most appropriate to do if there are special circumstances.

Of course this is not about converting specifically but just about being mindful of one's practices when there are special circumstances.

On the other hand, some mental health conditions push people to consider spiritual matters more deeply than they would have otherwise. 

May Allah grant them healing and inshallah also intercession of Ahl Al Bayt (a).