*If the rational thought process was internalised, so that it was performed subconsciously, would it cease to be rational?
Yes and no, depending on which definition of reason you take. Two of the dictionary terms are relevant here
Rational:
using reason: no because it's subconscious.
based on reason; fitting in with reason; yes because regardless of the lack of mental activity taken on behalf of the person it is still a point of view that is based on reason.
The crucial difference is how you get to your atheism. What was your starting point?
If, like myself, you were brought up theist then yes there is an extended rational process that leads to the rejection of God. You look at the evidence for the religion, there is none, you discard the religion. All very rational.
If, like my son, you are brought up atheist then no you don't have to go through the same rational process because atheism is the default.
However, and this is a big however, every atheist is usually aware that religions exist, that people believe in God, that we as a country believed in God once, so every atheist goes through some kind of rational thought process when they internally reject the God of others. My son, for example, goes through this process every Wednesday when he has RS and has to sit and be respectful to faith-based religions and is not allowed to call "bullshit" (not that I wish him to be disrespectful but I would like him to be able to at least express his opinion without feeling guilty)
He comes home and says Mum how do they believe in abc when there's clearly no evidence for abc. He is being rational and I'm proud of him. Even "passive" atheists need to hone their arguments and thus engage their logic because they are surrounded by theists like your good self.
Would the experience of an internalised and subconscious rational thought process [for an atheist] be similar to the experience of faith? (Since evidence is nit consciously gathered or analysed)
No because faith is the suspension of reason which is required to continue believing in God when faced with the lack of evidence.
Now Spinnaker I've spent a long time writing this for you. Please have the good grace to respond to it!