Does crashing during a test mean you have to scrap the roller coaster?
Let's do some science to find out! Here's what I did: I created a new coaster specifically designed to crash. Upon testing, of course, it crashes. When I open it up, nobody wants to ride it because it "isn't safe" (note that if I didn't test it, someone probably would have gotten on).
From there, I made all of the changes necessary to make sure it didn't crash ever again, tested it, and re-opened it. To my surprise, the guests were still convinced the ride was not safe, even though it wasn't designed to blow up this time. From this result, we can conclude that yes, crashes during testing do, in fact, matter. But there are a couple of ways to prevent them, or fix the problem after-the-fact if needed.
If you suspect your coaster might crash during testing, hold your mouse over the "close" button, and watch closely, especially in the section you're concerned with. If it starts to fly off the track, double click the "close" button to stop it. If you're quick enough, you'll close and reset the ride before it starts actually crashing (it doesn't count if things haven't exploded).
If you aren't fast enough, and your design is strictly above-ground, you can save that design, remove the whole thing, and replace it. That way, you won't have to start all over.
If your track did have some underground sections, then it gets complicated, since when you place a saved track, it tries to put the lowest point on the ground. At that point, it might be best to start over.