I'm pretty sure I have seen situations where my inquisitor flipped the city back to my religion, so it must be converting some portion of the influence it removes.
No... your pressure was already there.
If a city has 20 pop
No religion 150 pressure
Your religion 250 pressure (1 follower)
Other Religion 3000 pressure (15 followers)**** its following this one
Other religion 600 pressure (3 followers)
(4000 total pressure... 200 per follower)
and you hit it with an inquisitor.....
it is now
no religion 150 pressure
Your religion 250 pressure (12 followers)***** its following your religion now
400 total pressure.. 20 per follower
Your pressure can seep in from trade routes or nearby cities... you just have to have enough to overcome all the other religions+"no religion"... an inquisitor removes all the 'other religions'
but that inquisitor won't help on a city that has not been exposed to your religion.