Does washroom silicone caulk turn into goo after time?
Yes. Silicone caulk has a surprisingly short expiry date.  My nonprofit has loads of the stuff all over the shop; people love to donate it when it's expired. Into the trash it goes.

It is degraded and will not work. It won't take longer to cure; it won't work at all. 

If the stuff is not behaving as you expect, don't chance it.  Bad caulk is like bad paint: It will ruin your project and make you spend hours cleaning it off for good product to stick. 

The caulk tube certainly has an expiration date stated on it. If it's not obvious, try rotating the tube in the caulk gun.  This date is valid if it's stored at room temperature - if it's stored in a hot attic or cold garage, all bets are off.   

If it's so old that no expiry date is stated, then it's way too old.