Well, I wouldn't want Sara to play with Vartann's feelings like that. That would make me dislike her a lot.
I could actually see it going both ways. Vartann is slightly more grounded, but Sara is very impulsive. I can see him walking up to her to ask her out, and I can see her getting so sick of doing nothing with her life that she'll just walk up to Vartann and ask HIM out.
I've never been a fan of GSR. Sara has wasted so much of her life chasing after a man who doesn't seem half interested. He's cold and sometimes downright calloused to her. I think she should be with someone who treats her like a queen. She deserves that. Vartann opening the door for her in Mea Culpa, that shows how attentive he is to her needs (they were on a hill and she was having a hard time getting it to stay open). The fact that he was also okay with her clearing the house with him also shows how much he respects her and trusts her and her abilities (while Brass, Grissom, etc, always treat her like a little girl who can't do anything right in a man's job). I think Vartann could be great for Sara. All the men in her life have treated her so badly.