Will a track wheel work with the dropouts on my frame?
Track frames use a 120mm rear dropout in most cases. 

You do have a horizontal dropout, but not a track dropout. It will work, but it is not ideal. 

The rear axle outside locknut distance on that frame is likely to be 127mm. 

Again, it is not ideal to compress the dropouts that much, but given that it is an older, fatigued steel frame, it will likely work.

Worst case, you might induce cracks in the frame over time, due to stress on the welds from the compression, but it isn't likely.