Wiring C-wire in old Rheem
No, the loose blue wire is a 208V tap. The C wire comes off the other side of the transformer. I highlighted the blue 208V wire you referenced, plus the C wire (yellow) in your schematic:



It's one of the two yellow wires, which go to another area (not pictured)



It actually doesn't make a difference which yellow wire is which (AC voltage, so no polarity) -- one goes to the "R" terminal (power, usually red) and the other is "C". From the schematic, you might have only 4 terminals for the thermostat, but there at least does appear to be a hookup for the C wire.