Can blepharoplasty procedure be done with someone who has permanent eyeliner?

There should be no issue doing an upper and lower lid bleph with permanent eyeliner. The only time there may be a problem, if the liner extends upward on the upper eyelid laterally, then a portion may be included in the lateral portion of the incision. 

Generally having permanent eyeliner will have no effect on successful eyelid surgery.  An experienced and talented surgeon will assess whether the eyeliner will unmask some pre-existing asymmetry and will plan accordingly. 

The blepharoplasty incisions in the upper eyelid are in the crease and in the lower lid just below the eyelashes or on the inner surface. Since the tattoos are near the eyelashes they aren't significant for upper blepharoplasties though they make look wider after surgery. For the lower eyelids if the incision is made on the inner surface the tattoo is irrelevant. If the incision is on the lower eyelid skin it may be okay depending on the width of the tattoo.