It sure does. Buying old paper, or storing it for a long time is usually a bit of a crap shoot.
I have found, however, two solutions to this, one of them via APUG member RLibersky.
1. Defender 58-D print developer. You have to get the ingredients yourself and mix them. But this thing suppresses fog and gives a pretty nice print on very old and expired paper. Libersky regularly prints on papers that expired in the 1950s and earlier.
2. Lith printing. Some of the older papers do well in lith printing, and since you overexpose the print by a factor of 4 to 10, the fog plays less of a role in the finished print. I was gifted a stash of 1980s Agfa Portriga Rapid that fogs up helplessly in Ansco 130, Ilford Multigrade, and Amidol. But it works very well with lith chemistry.
I think it was Ilford and Simon Galley that latest talked about paper aging on APUG, and the number of 5 years for some reason wants to make itself heard here, but don't hold me to it.
I think the decline of the paper qualities is gradual, so it gets gradually worse, but for a certain time period it will stay within specification. I think it's best to use the paper fresh if you can.
With that said, many interesting effects can be had with old paper, but it's usually not repeatable.
Good luck.