It can, and it probably will.
A lot of jobs are coming down on those who get visible tattoos on forearms as well as other places that aren't usually covered up.
I had to sign a form saying that I do not have any visible tattoos on my body while working, otherwise I wouldn't be welcome to work there.
Meaning that if I got a tattoo done after the fact of me working there, they would probably fire me.

I personally wouldn't do it because a lot of people and employers are highly discouraged by it.
You would never want to jeopardize a possible good job opportunity for a bit of ink that you could get on a less visible spot of your body.

Edit: It would also help if you were to ask your employer what his views on it are. Then you would find out for sure before possibly sticking your foot in a trap.
Good luck though!