do cheap bull barrels shoot?

[Great-Kazoo]

I guess I'd like it to shoot 1" or less groups at 100yds with hand loaded ammo.

I would mostly use it to punch paper and maybe shoot some p-dogs.

An off the rack factory build can do that. As mentioned before, load development.

[TheBelly]

http://youtu.be/HHcSQ3d7nVY

93m .4" group from a 16" Rainier Ultra Match barrel.

[davsel]

I've shot my best groups with an AR Stoner barrel (18", Stainless, 1 in 8, mid-weight, fluted, Wylde chamber) from Midway for just over $260.
I've also shot great groups with a Rainier (16", Stainless, 1 in 8, mid-weight, Wylde chamber) from Rainier for just over $250.

"They" say coated barrels, chrome or otherwise, can have varying thickness of coating, which may lead to less accuracy.
"Others" say not.