Sure it will run with the rocker cover off, all the rocker cover does is keep the dirt out and oil in.
If you want you can take a spare cover, and cut the top out, it allows you to work, but also contain most of the oil. When I did a compression check on my 4 cylinder it did not make a mess, just left the cover off completely, it only needs to run for 5 or 10 seconds per cylinder.
Yes, the biggest part of a "tuneup" is adjusting the valves and injectors, also the governor if needed.
Grigg
