As others have said, I don't think there's a real hard and fast rule on this. If your friend's family is very private they may be offended. If they are more expansive, they may be touched and pleased.
I can only speak from my own experience, but here's what happened and how I felt about it. When my mother died, a very good friend of mine had to travel a long distance to come to the memorial, but she arranged the time off work, the travel and everything because she had been nearly as close to my mother as she was to me. It was important for her to be there, and it meant a lot to my family that she went to so much trouble to be there.
She had been dating a guy for a couple months then. None of us had gotten the chance to meet him yet, and she wasn't sure it was okay if he came along, but he was determined. He was worried about how broken up she was and wanted to support her. Everyone in my family was deeply impressed with his willingness to put himself in what must have been an uncomfortable position to help her cope at a difficult time. In between making sure my friend was okay, he quietly helped the whole family deal with little things we were too spaced-out and confused to think of. He didn't intrude in any way, but he seemed to notice things like when plates were emptying at the wake and when one of us didn't seem to have eaten or drunk anything for too long. He'd take a platter into the kitchen or nudge a glass nearer one of our hands, or bring a box of Kleenex a little closer. Just little things like that. We were grateful.
Oh, and my friend and her boyfriend? Have now been married for nearly twenty years and have two beautiful children. He's a terrific guy. I knew it the first time I met him.