Is it possible to effectively dissolve chocolate into coffee?
One classic solution is to make a ganache to make the chocolate liquid. Ganache is an emulsion that suspends the cocoa butter in water which helps it mix with the coffee. While this sounds fancy, you can make it in a few minutes.
The recipe I use is from The Blue Bottle Craft of Coffee by James Freeman

Put 3 oz (85 g) coarsely chopped dark chocolate in a small bowl
Pour 1/4 cup (60 ml) boiling water over the chocolate and stir until smooth
You can pour your coffee directly over the ganache or store the ganache in the fridge for up to one week. Reheat in the microwave (gently) before using.

The original recipe uses espresso and tops the coffee with hot foamed milk. I have also always used espresso and foamed milk, but I believe coffee should also produce good results. If you don't use the foamed milk, I suggest using a less dark chocolate to balance the bitterness.
Ganache can also be made with heavy cream instead of water. I have not tried using a cream-based ganache in this drink.
One note is that this recipe works best for hot drinks. Cold drinks can seize the chocolate into lumps.