Ilia didn't share her blood with Chekov, she used some form of mental ability to suppress his pain while Chapel was the one who actually healed his electrical burns.
This would appear to be the case, yes. But ... the physical contact displayed - and apparently necessary - was very reminiscent of the Mugatu Witchy Woman from TOS, who used a root to give Kirk a strange transfusion and instantly cure him. I'm not saying that's what's going on, here, but Ilia's stacking her hands on Chekov's shoulder reminds heavily of it. There may be further implications, there. Well-worth investigating, considering recent theories on Ilia's blood properties ...