It sounds like repair estimates are going to be freely available so I wonder if YourMechanic becomes a reference-able source of quote information for negotiating purposes?
No. Repair estimates are already freely available. Just google the parts you need to replace. The price you see (plus taxes) should be what you pay to your mechanic.
Unless you're getting major work done (i.e., dent removal), a reputable mechanic will only charge for parts, not for labor. If you've never actually had that experience with your mechanic, I suggest you look around b/c you've been getting ripped off.