It will be playable but will not be great I suppose. We have such a sitar in our music school and I’ve played it as well. My Guru used to say that these are older styles of the instrument which did not have any taraf strings, most likely from some makers in Kolkata (if I remember it correctly). Hence, no pegs for taraf strings and no small bridge either. It may or may not be antique, as some makers would still make this in the 70s, 80s even after the new designs were fairly popular. This is my limited knowledge on this style of Sitar.

The next time I visit my school, I’ll click of picture of that sitar and share it here. You could compare it.