Having one thread print while another reads console input

What would happen if I called print after calling read on a different thread?

ComputerCraft and Lua, as far as I know, doesn't support multithreading but rather you can take advantage of the parallel API which implements coroutines to mimic simultaneous execution.

Using 'parallel.waitForAny(print("TEST", read()))' would result in the print statement being executed first and then the read would be executed.

Hope I helped! :)/>/>

So I can't print something while trying to read()?

Yes, but it wouldn't be at the same time. It looks like it's running at the same time but it's not.
You can use:

local function printStuff()
  while true do
	print("Some text here")
  end
end

local function getInput()
  while true do
	local input = read()
	-- do something with input
  end
end

parallel.waitForAny(printStuff, getInput)

But you have to take care of the functions not overwriting each other's text.