I decided I couldn't wait to test this. I have two of these New Home machines and maybe 6 bobbins between them.
The pictures aren't so great, but here's the result, stitched just fine, had to tweak the upper tension of course (purple thread is upper, green is bobbin). The machine I tested on is not very fast, so high speeds could make a difference. One potential hang up is winding a bobbin. This test machine has an "open" bobbin winder, the 301 bobbin fit tightly enough to not spin on the bobbin winder spindle; the small hole to lock the bobbin did not reach the small pin on the bobbin winder. My concern for a machine with an auto stop feature on winding a bobbin is that you might not be able to get the 301 bobbin mounted correctly for the auto stop "tongue" to fit into the bobbin.
This is actually great news, now Janey if you can only tell me how 15x1 needles will fit this all will be well in my small sewing machine world.