Impossible to say without trying it, (from the photos I can't even see if it's real wood or laminate or if the finger board is ebony or painted "hard wood") but without a sound post you can't try it!
Retrieving / Replacing the sound post is quite difficult and you're talking £100 or so to get it replaced and properly set up. That or many hours fishing about inside trying to snag it with a loop of fishing line and many hours more tweaking it about 'till it sounds right.
(edit, bloke on another thread got his music teacher to replace the post for a tenner ... so I overestimated a bit!)