No a tattoo will not deny you a class 1. The only people to worry about is the employer, but if the tattoo will not be on show wearing a pilot uniform then it's ok. Problems start when you have tattoos on your neck, face or a whole sleeve.
It sounds like your tattoo won't be visible with a shirt on so it's fine.
I was led to believe the reason they ask for tattoo might be for body identification. I could be completely wrong but that's what a friend said.