If driver #17 does not set a time within 107% of the leader’s time in Q1, he will not qualify for the race, and thus will not advance to Q2.
If he makes it to Q2, but sets a time outside 107%, he will be entitled to race. The 107% rules is not designed to weed out drivers who are slow. It’s designed to prevent teams that are not fast enough to race from making the grid.
There’s also the possibility of appeal. If the driver qualified 17th is blocked or there’s some other legitimate reason why their time was slow, they could be allowed to race. However, they probably won’t be participating in the rest of the session, instead they’ll line up at the very back of the grid.