I've shot a few woodswalks with a jag attached to the RR, sticking out beyond the muzzle (but below it), mainly because the length it added gave me more to grip. I couldn't tell any difference, but it would be the type of thing that might only show up off the bench on a target. It made me nervous (just sticking out there, asking to hang on something), so I usually shoot without the jag on the RR, anyway. If your RR hole is short, however, and you don't have any choice, I'm pretty sure it will not RUIN accuracy, at least for woodswalk type shooting. I've never thought about shooting without a ramrod in the pipes. It might indeed be worth trying, just to see what happens.
One other note. Some NMLRA matches require a ramrod or something that looks like a ramrod. I don't know if the simple provision for a ramrod would suffice, although I can't see shooting the rifle with the ramrod absent would be an issue.