No. Bella has known he is immortal and so she suspects he is very old and that hasn't affected their relationship at so why should it make any difference now. If anything Edward's age is good because he has been waiting for that special someone to come along for so long that now that she did he is capable of loving her that much more than any human could

2. Edward tells Bella very little about the process of becoming a vampire. Why do you think he chose to keep this from her when he is being so very open about everything else?
Obviously because Bella always surprises him with her views and opinions and he doesn't want to give Bella any ideas.
3. We learn that many vampires are gifted with supernatural traits. Stephenie has told us that vampires are drawn to special humans, and therefore when those humans become vampires, their special qualities are enhanced. If that is the case, I simply must ask the question everyone one of us has asked at some point. If Bella were to become a vampire, what would her trait be? And is it possible for her to not have any special trait at all?
Maybe some kind of mental barrier because Edward can't read her mind. I don't know, but maybe.
4. Edward lets it out that he's been watching Bella as she sleeps. Again, did this creep you out or make you fall even harder for Edward?
This made no difference to me, I didn't fall for him because I am a guy lol, but I can understand why he would do that when he can't sleep and lives forever and now something new and beautiful has been inserted into his life, something that he loves, you can't blame him for being curious.
5. Edward says two possibly conflicting things in this chapter. First, he explains that in the last few days, he has put mind over matter and has been able to control his thirst for her - that the temptation isn't as strong. He later says that he doesn't think it would ever be possible for them to have an intimate relationship because it would be too difficult for him to control himself. Do you think he's being honest with himself, or do you think he's just trying to protect Bella again?
He is always afraid for Bella's safety and he isn't sure how intimate he can be and still keep Bella safe and he won't take a risk like he did when he kissed her again because he can' stand to put her in danger.
6. Along those same lines, we learn that both Edward and Bella have never had a real relationship with another person before this. Many people have debated the issue of Edward's virginity, and that has been put to rest by Stephenie herself. Did you think that maybe Edward had been intimate before, he just hadn’t had a real serious relationship with anyone he loved, or did you get it right from the start that he was just as innocent as Bella was in this matter?
Just as innocent, before Bella, he thought he was complete in himself never searching for anything else.