Are there any issues with running a vNext build agent on the same machine that is running Functional Tests? My plan is to have an agent pool that consists primarily of test machines where each build agent has a one-to-one relationship to running functional tests on each respective machine.
Yes, you have the ability to run some Unit Tests both on a machine different from that one is running the build and on the same machine.
To select build agent in a pool which include multiple agents:
You can add a User Capability to that specific build agent then in the build definition you put that capability as a demand (General tab)
How to specify a build agent in vNext build
About how to configure build pipeline and deploy test agent, you could refer below tutorials:
Hope this helps.