Can i use a power line adapter to use my work computer at home instead of running a Ethernet cord thru the house?

Yes, provided you can ensure that the two adaptors are on the same phase of the mains electrical powers upply - which they usually will be in ordinary domestic properties.

The Powerline adaptor pair is effectively a direct ethernet connection between the two ends.

Q.  ... power line adapter to use my work computer at home instead of running a Ethernet ....

A.  MAYBE -- You can buy a pair ( https://www.amazon.com/Tenda-AV1000-Gigabit-Powerl... ) and see if it works.

It is TRIVIAL to run an Ethernet connection between two points in any house.

powerline adapters do not work well, and muddy up your electrical signals. better to use a wireless access point.

It depends on where the router is, and where you want the other end to be. If they are on completely different circuit breakers, you won't get a signal. You'd be better off setting up wifi (if that's possible) and if it's not possible, hiring someone to runt he ethernet.

What a power line adaptor does is to turn your wiring in your house into a large antenna to transmit the Ethernet signal through the whole house. the only way to know if it will work is to install one and try it. Depending on the wiring, the signal going over it may or may not be strong enough to run a VPN that you would need to reach back to your work network. None of us can predict what the wiring is like in your house.

I'm not sure what your "power adapter" is, but if it isn't an RJ45 it won't connect to the outlet 

You can set up a wireless hub if you want to

You would need to make sure you get one fast enough for your internet connection.  Ethernet is cheaper and faster if you can put the work in, but a lot of people use the powerline adapters if the run is too difficult.  Getting a wifi router rated AC1900 or higher might be a better investment if your current wifi is not adequate for a work VPN.