You can't know if it will last.
A lot of people who get married so young split up.
Some make it.
They might make it, maybe they will be together until they die. Maybe they will get divorced in 5 years.
You can't know that.
Practically speaking, I would be sitting down to talk with both of them. What are their plans? How do they want the wedding to be financed? What will they do in terms of living arrangements? Do they want to live with a parent (not acceptable in my book)? Will one of them get a job? How will they pay the bills? Will they finish school/college? Do they want to have children?
Maybe they have thought it all out, but maybe they haven't thought of all the practicalities. I think that if they want the "romance" of getting married, then they need to consider the practical aspects as well.
If they have plans for all this, if they have thought it through, then I would support them and give permission.
Be aware that they could elope anyway, that if you arbitrarily remove support then you could drive them away and damage your relationship.
I was in a relationship at 17 and I wanted to marry him. If he would have asked, I would imagine that we would have been married. All I can say is that nothing but the power of hindsight will make them see that it is not right (IF indeed it is not).