Yes, shape and chord matters when it comes to propellers.
I think I've told the story before, but I had a Grumman Traveler with a brand new McCauley cruise prop. During my annual inspection, the shop (a noted Grumman 'guru') had another Traveler parked next to mine. The owner had brought it in to "get the engine fixed" because he was not obtaining anywhere NEAR book performance. The IA kept telling him it was his worn-out prop that was the issue, and that the engine was fine. But the owner insisted that a propeller shop had overhauled the prop and told him it was "just fine" as it was...
Looking at the two planes parked nose to nose, his propeller looked like a toothpick compared to mine. It had been filed down so much along the entire length of the blades that it was at least 3/4" narrower than mine, and was substantially "thinner" as well. It had apparently been filed repeatedly to remove dents and dings over the years. Aerodynamically, it was a complete mess, having so much chord and camber from the profile. I honestly have no idea how a competent prop shop would have ever signed off on that prop as being airworthy. Even seeing the side-by-side pictures, the owner simply refused to believe that his poor abused propeller was the reason his airplane was waaaay slower than book...
Since we had to remove my prop anyway to fix a leaking front seal, the IA asked my permission to temporarily install my prop on the other guy's plane, and take it up for a test flight with the owner. As soon as they landed, the owner forked over the money to buy a new prop for his plane.
PS - The labor cost for replacing the seal on my engine got "comped" by the shop, since they sold the new prop to the guy. Good deal all around.