Should I go?

My ex and I have known each other for a very long time and we're good friends growing up. We dated for 2 years and lived together at one point. But eventually our relationship just blew up. We weren't good together. We're still friends and he's helped me through a lot. I saw him back in December and he had broken up with his girlfriend some months prior and was really hurting. We ended up sleeping together. No big deal and I don't want him back- he was just there and he was framiliar. He ended up going back to his girlfriend. Which I think is great because even though I've never met her, I can tell that he really loves her and is really good for him. I know she knows what happened between us. 
Anyways, he was in a very serious car accident. He's in critical condition and things not look good at all. I want to go see him and just be there for him in any way possible. My only concern is that I know his girlfriend will be there and I really don't want to overstep. From what I know about her she's very nice, but I know for a fact that I slept with her boyfriend (even though they were broke up at the time) really upset her. She doesn't mind that I'm friends with him, but I know she doesn't want anything to do with me. I'm worried I'd overstep by going to the hospital. I don't want to make this situation any worse for her than it already is. She is his girlfriend and I'm an ex  so in my opinion she gets to be the one that's more affected by this whole situation and I feel I should do what I can to make it easier for her. But I really want to see him. Any advice would be really appreciated! And if you read to the end thank you- I know this was really long! Thank you