I don't have any hard evidence or numbers on how progress bars affect abandonment rates. But I can give my experience on the subject.
I worked on a website that had a 15-20 minute long insurance application. That site was my responsibility for about 6 years, and I saw it go through a lot of changes.
We had a progress bar ever since the beginning though. In the early days you would see the progress bar from the very first step. It would say something like "6% complete." Eventually we changed this, and I'll tell you why.
As we optimized the site we found that users are more likely to abandon in the very early stages of the application.
Starting from the beginning, the abandonment rates for each step went something like this:
- 40% abandon
- and so on...
What we were probably seeing is that the more serious users tend to follow through with the application. And most of the users who abandoned early on did so because they weren't really serious anyway. On top of that, we had the traditional friction points early in the application such as registration, where we ask the user for their email address and contact information.
So because of these figures, and the fact that the registration page had a very high abandonment rate, we actually changed things so that the progress bar is invisible for the first few steps. And then it appears on the step after the registration page. At that point it'll say something like "25% complete." The theory was, just as you said, that the progress bar might actually be scaring users away early on in the application.
We changed a lot of other things at the same time, so I can't say for certain what an impact this might have had, if any. But maybe it'll help you anyway.