It's going to depend heavily on the rest of your appearance, what the tattoos are and their quality.
We've got guys here with titties all over their arms and :censored::censored::censored::censored: like that, stuff that looks like it was done in a flop house, just ugly tattoos. I've spent thousands of dollars on my arm sleeve alone and my managers hate that they have to make me cover it because "it's so pretty" hell almost every patient that's seen it has complimented me on it but they have to have a uniform enforcement of the policy.
It sucks man, it's bull:censored::censored::censored::censored: that we're judged by our appearances. I'm sure you get it worse than I with your neck.
I'm sure there are places out there but you're not going to have the luxury of being picky or really choosing where you live if you're dead set on a job as an EMT.