Should my thermostat's blue wire be going to W2?
Almost every thermostat installation manual I've read always says something along the lines of "Make sure to mark you wires based on the currently connected thermostat. Do not rely on the wire coloring".

The colors are really just a guideline, there is no requirement to adhere to them.

Looking at the controller board of your furnace should confirm how they are connected.  It's possible that the blue wire isn't even connected to anything on the furnace side.  Perhaps the furnace was replaced at some point and the thermostat wasn't re-wired.

It's not uncommon to not have a C wire as older thermostats were either unpowered or powered by batteries.  New thermostats (especially the ones with LCD screens, Wifi, etc.) have larger power requirements and rely on the C wire to provide a return path for power coming from the R terminal.