Increase working hours for an external speaker
Connecting an additional (preferably identical) 18650 would theoretically double your capacity, yes. However, there are some safety concerns you need to address first. 


Does either 18650 have built-in protection? This can be a huge issue if that controller shuts off one battery but the other keeps discharging, due to reasons stated in the next point
Are the cells at an equal voltage? If not, connecting them in parallel will induce a massive current from the higher-charged cell. If the difference is too great, this current could flow for a while and overheat the cells


The safer way to do this is to connect two identical unprotected cells at the same voltage in parallel, then hook up your protection circuit to that pair. In your case, I'd bet the protection circuit is somewhere on the PCB for this speaker. 

To address point 2, typically charge controllers check that the cell voltage is above a threshold, say 4.2V, at which point it will disconnect (cheap ones will trickle charge after 4.2V but this is supposedly bad for battery health). Your charge controller likely doesn't care about the capacity, so while it may take twice as long to charge, the charge LED should work as intended all the same.