As a musician who is also a bit of a videogame soundtrack nerd (I would unironically listen to Jazz Jackrabbit in the car)... yes, I would still try the game. Some games are fine, or even better without music. I guess if I was playing and the whole time kept thinking to myself "I wish there was a soundtrack", then the game might feel unfinished.
I'd say that if you're leaving out the music then make sure the rest of the audio design does a good job of filling the space, as you probably should avoid complete silence most of the time. Music helps with that since even when nothing is happening in the game, there's some audio going. Just having some very ambient thing going on, that people argue if it even counts as music, will help to ensure that it's never completely silent. From a sound design perspective, complete silence is almost always a bad thing. It's especially jarring to your ears if you are on headphones and go from silence, to a somewhat loud sound, or vice versa. You may have experienced a "rumbling" in your ears if you've ever done this (listening to loud music and you suddenly pull out the cord), because our hearing is relative, and always trying to adjust to the overall volume. This is why in professional music production there's almost always some amount of sound throughout the song, even if it drops to very quiet it will never be completely silent (well, almost never).
Now despite being a music nerd who will listen to the OST even when it's kinda bad, I have also had some experiences where I enjoyed no-music gaming. A great example would be Abuse... I always played this game without music! It actually does have a soundtrack but I either couldn't get it to work or had a version where it was missing. Now when I look at gameplay videos where the music is working, it just sounds cheesy to me. To me this game is actually better without the music because the sound design together with the grungy visuals creates the perfect atmosphere. Of course I'm biased since I always played it without music and therefore when I hear the music my brain is like, what? Anyway my point is, you should feel free to not include bumpin' tracks in your game if that's going to achieve the atmosphere that you want.