1. It's neither appropriate nor inappropriate.
2. Positives are you get a hotter ignition gas and a greater volume of ignition gas; however, with real black there's no need for hotter or more ignition gas. Some folks who have dexterity issues (ie, old farts like me) find them easier to handle, especially in cold weather. Negatives are the conversion costs money and the caps are more expensive - not a great deal of money, but hey, for us old farts pennies matter sometimes.
As far as PC is concerned, musket caps are not all that modern themselves, and a T/C "Hawken" isn't necessarily all that PC itself. It is a plains style sidelock, which is a very good thing, but a Hawken it isn't.