I think that the hard part about receiving a diagnosis at 17 is that when you feel different from other teens, it is hard when someone confirms that difference. The last thing a teenager wants to do is admit that she'll never be everyone else's version of "normal". It's just really hard being the "oddball".
I think the best thing you can do is to be open to her questions and thoughts. Be honest about what you observe, but don't push her to accept a diagnosis before she's had a chance to test her own limits. Saying things like, "I think you may be taking on too much right now, it's okay to step back and reconsider if things are too stressful" or "I think you may be missing something important your friend is trying to communicate" are ways to acknowledge some Aspie tendencies without always pathologizing them, or emphasizing her difference.
With experience, she may realize that her needs are different from others, and if you have offered her an open dialog without injecting your preconceptions, she may indeed acknowledge if the diagnosis fits. But at 17, she is still discovering her own identity, and it's natural not to want to impose what she may perceive as limitations on that identity.
I understand your concern, though. I was without a diagnosis until age 34; until that time I struggled with jobs, college, relationships, and family, for reasons that have only now become clear to me. I wish that I had known about my condition much earlier. But by the same token, it was those struggles that helped me to realize and acknowledge my diagnosis. I don't know whether I would have "bought" it at 17. But if I had known something about ASD, I might have come to accept my differences sooner and may have felt empowered by that knowledge, rather than hindered.
The upshot is, that for a diagnosis to be helpful, she has to be open to it, and ready for it. Most of us who received a late diagnosis, on first hearing our diagnosis, for a period feel both anger and denial. Later this denial may become self-doubt. It's the result of having so many questions that had gone unanswered or unexplained for so long.
She would be very welcome here, but she will only feel welcome if she feels like she has a reason to be here, so for now, your presence here will benefit her indirectly, as you learn ways to engage with her and support her as she tries to find her way in life. She is fortunate to have a father who cares so deeply.