The one time I caught a train on that branch, in the summer of 1968, it was a backup move. The short local freight behind an Alco switcher left East Deerfield engine-first, headed down the connecting track to the ex-NH trackage, reversed ends, and shoved to Turner's Falls. I presume they came back engine-first and backed up into the yard. At the time there was a small paper mill or box manufacturer along one of the canals in Turner's Falls that got a boxcar or two now and then. The B&M freight house was also still standing but I don't think it was occupied by then.
As Mr. Geep notes, the B&M took over the former NH line into TF when the NH abandoned it north from Northampton in 1943, and abandoned its own line at that time except for some of the terminal trackage at the north end. The secondhand nature of the B&M's branch in its later decades was the reason for the awkward switchback connection at East Deerfield.