It might to some extent, but it's not the perfect way to go.
Speech reproduction gets muddled by distortion and by masking ( https://en.wikipedia.org/wiki/Auditory_masking ).
If you have one speaker reproducing both speech and other sound, this is what happens:
1. additional sound output means heightened distortion
2. when two sounds come from two places, our brains can separate them due to phase differences and spatial perception, so those two sounds mask each other less than if the same two sounds come out of a single speaker, even if it's perfect, with no distortion etc
3. the speaker is made for broad range reproduction and not voice reproduction, so it'll de-emphasize speech frequencies, which are exactly those frequencies that also make music sound like it's coming out of a cardboard box. ultimately the applied eq (equalizer) curve will create speech that's slightly muddy, like someone talking from behind a blanket.
4. sound bars use tiny transducers which are woefully underpowered compared to the SPL (sound pressure level) they're tasked with producing. This is done by using multi-band compression and limiting. This sometimes creates situations where the limiting might be recovering after a slightly louder sound, and the very next syllable will be muted.
However, having a dedicated speaker for the center channel is none the less way better than not having one at all. If that's all you can try, you can try your luck. But be aware that getting a cheap one will probably not get you where you want to be - you'll have to spend a pretty penny. At that point if you have the space you might want to get a 3.1 bookshelf speaker setup. They don't have to be very large to provide great value-for-space-used.