That's an "it depends" question. Some Bluetooth speakers simply sum the music to mono, like the small Philips speaker I own. Others that claim to be stereo will have a left and right dirver, yet will still share a common bass speaker to save space. (My Scosche Boom Bottle does this--it's a Bluetooth speaker designed to fit bicycle water bottle holders, for those times when tunes are more important than hydration.) For something more advanced like the Riva Arena speakers, they have drivers on the front and both sides, and use their own technology to present a wide stereo image by way of how the speakers are driven. (A pair of Arenas can also be configured as left and right speakers, but only through the Chromecast option, not Bluetooth, as Bluetooth audio can only make one connection at a time.)
Yes, they all should be. The two sets of earbuds I have are both stereo. Bluetooth isn't the best fidelity (it's lossy/compressed, basically like MP3), but for my purposes, it's good enough to take a phone call, have notifications read to me, and play music just loud enough to drown out the crap the stores play.
If I ever need to do serious listening on headphones using a phone as a source, I use an Audioquest Dragonfly and my planar headphones (made by Oppo).
