The carbonation drops will dissolve in the beer but can sit at the bottom in a thickish, syrupy layer. The yeast floating around in your beer will eat it up in time and in doing so will carbonate your beer, but it make take longer.
A good idea is to go back the day after bottling and just give the bottles a gentle upside-down turn to get the sugar up off the bottom and mixed uniformly throughout the beer. This makes it much easier for the yeast to do their thing.
Also, after bottling store the beer room temp (~20C) so the yeast are active and get straight to work. If you store freshly bottled beer in a cold shed or room it might eventually carb up, but it can take a longer time.
Good luck with it.