How can I hack a Bluetooth mono headset into a speakerphone?
A 3.7 V peak to peak sine wave into 8 &Omega; only delivers 214 mW of power.  That's not likely enough for something usable as a speakerphone.  If you do a double ended driver, then you get twice the voltage and therefore four times the power, or 850 mW.  That might be enough depending on how loud you want this to be and how effecient the speaker is.

You don't say where this 3.7 V comes from, but it sounds like it might be from a battery.  Wherever it comes from, all you know is that the power system was designed to handle the requirements of the bluetooth unit.  You don't know how much extra power it can put out, if any.  You probably want to plan on the audio amp to be at least capable of a few watts peak, even though you will run it well less than that most of the time.  The additional power to drive the speaker has to come from somewhere.

A number of manufacturers make small class D audio power chips designed to drive small speakers effeiciently from common battery voltages.  I recently had a similar requirement and ended up specifying the On Semi NCP2820.  I haven't gotten built boards back yet so I can only say it looks good on paper at this point.