Can I wire a 3 way switch to a light but also have an always-hot receptacle?
Due to the way the three way switch is wired, you will not be able to do this. Either, your outlet will turn on and off with the switches, or you would essentially render the switches "Always On" (By connecting both travelers together in the outlet). Regardless, your best option is to run a new line to the outlet. See the diagram below:



You should be able to daisy chain off a nearby outlet so you don't have to go all the way back to the breaker box.
Good Luck!