Is it a bad idea to boil black jelly beans?
a) Jelly beans are made of sugar, starch, flavorings, and pectin.  As such, it's fine to boil, mash, roast, fry, steam, or really do anything you want with them. The worst possible consequence is them sticking to be bottom of the pot and being hard to remove.

b) First, black jelly beans are generally flavored with licorice and not anise, and star anise tastes different from anise seed.  So this would definitely be a case of substituting a distinctly different, though similar-tasting, spice.  Second, a single jelly bean is unlikely to have enough flavor to affect the flavor of the broth; you would probably need to add several.

So, my recommendation if you really want to try this is to use 6-10 black jelly beans, wrapped in cheesecloth or in an empty tea bag so that they don't stick to the bottom of the pot.  And tell us how it works out!