Yeah, it can go bad just like any other light sensitive material. Does it go off faster than RC paper or vice versa? I don't think so. It's the stability of the emulsion that counts for more than anything else, and the emulsions are pretty similar on RC and FB papers of the same brand and type. DaveOttawa's suggestion is one of the better ways to test the paper short of making a print on the old and new paper of the same brand and type. Comparing a print made on fresh brand X paper to one made on old brand Y paper tells you nothing conclusive because the two papers may be very different at the start. Take a sheet and cut a couple of strips from it. Run one unexposed strip through the usual process. Run another only through the fixer. After a quick wash and dry, compare them side by side. Assuming that your safelight is safe, any difference will reveal that there is some age fog present.
By the way, there is nothing particularly difficult about using FB papers. They can be a little more difficult to handle when wet (it is a soaking wet piece of paper after all), will exhaust your chemistry more quickly, won't dry flat most of the time, and will cost more to buy. When I first started printing, RC papers were the new technology, not very good, and commanded a premium price. Needless to say, I did most of my printing on Kodabromide grade 2, single weight glossy. When RC papers improved to what they are now and I started using them, it was like a miracle - no more worries about creased, torn, and wrinkled prints. All that and a two minute wash cycle. What's not to like?