MarinerMB :
After much research on my own I found the answer and I wanted to share this answer in case anyone else was researching:
Actually the answer is NO.
Only a bluetooth with A2DP technology can stream sound (music, voice text, etc). Athough I'm sure there are others, on the market today I found the Plantronics Pro +, the blueant and the Jawbone icon.
Hope it helps someone
Thanks for your sharing, it does help me to look for a solution the other way round.
As the FAQ from the official site says 'If your phone transmits audio through the voice channel (SCO), you may be able to establish a Bluetooth connection between the Jawbone and your mobile phone and play your audio file' <-- I guess some old Nokia phone can do it, at least my 6210C do.
For Android phone, try the app "btmono", it would enable you to switch between channels, though the sound quality would down graded in narrow voice bandwidth, it's better than nothing.