Immunochemistry experiment involving hemoglobin F

Hemoglobin A has two alpha chains and two beta chains. Hemoglobin F has two alpha chains and two gamma chains. Hemoglobin Barts has four gamma chains. Suppose you had one antibody preparation that reacted solely with the gamma chains and a second antibody preparation that mainly consisted of antibodies which bind to gamma chains but which also had some antibodies that could bind to the alpha chain. Would these two behave differently in an Ouchterlony (double diffusion) experiment involving Hb F and Hb Barts in two adjacent wells?

I think that they would. In the first case, you would see a smooth arc of precipitin from anti-HbF antibodies reacting with the gamma chains. In the second case, you would see a smooth arc, but I think you would also see a spur pointing toward the well containing Hb Barts. The spur would be caused by the reaction between the anti-alpha antibodies and the alpha chains found in HbF.

The reason for my question is that I am trying to understand the immunochemistry in the Lindy Chamberlain case. In this case the specificity of the anti-HbF antibodies was a very contentious issue.