I have Ehlers Danlos (Classic) and two tattoos. I did need a touch up due to my skin rejecting the shallow ink, but when the artist went deeper, the tattoo came out perfectly. I've had no health issues due to them, nor did I have any pronounced pain, so in my opinion yes, they are safe if you have EDS.
I have ehlers danlos type 3 (hypermobility) am 51 years old and have 7 tattoos so far (want more) Although mine healed very quickly and I've had no problems with them since, it does pay to ask your primary care supporter for advice too. I would think that if anyone had EDS4 it would NOT be a good idea to have inks done, but the other types should be ok.