It’ll work as long as there’s enough shank to work with. The big issue is the Bergara has the aforementioned coned breech, whereas the R700 design uses a counterbore.
The tenon threads are the same, 1.062” x 16 TPI, it’s just headspace and coned vs counterbored breech. You usually can’t take a barrel with one tenon thread pattern to another pattern because you typically have to chop the tenon and start over, and there usually isn’t enough shank left after you do that. Primary exceptions would be going from a very large thread diameter to something smaller, so you could machine down the threads and just cut new ones underneath, a barrel-nut setup with a very minimal taper, any barrel with an abnormally long shank, or a straight taper that is basically all shank.
But you’re probably better off just trying to sell the barrel and buying a Remage for your R700.