No, he's shown himself to be a single minded battle hungry moron who just got himself mangled and drew attention that I myself, would not want. In addition to causing us to get captured which (Unless that was what OL wanted) is going to force me to use resources and abilities that I might not want to use around fucking QWARDIANS to get free.
Why would I throw away this (In my opinion) failure of a recruit? Well, other than the failure part, he has also made the tragic recruitment mistake of pissing me off. Finally, there are trillions and trillions of lifeforms in the universe. I can find another, better recruit easily.
So Ragnar the dunce gets kicked out of the Red Lantern corps (I can't claim to be Orange) minus one arm and plus the ass kicking I'd give him just for pulling this shit.
While I think it's obvious that I'm not going to change your mind I think you're looking at it the wrong way. While yes, he has shown himself willing to throw himself into fights without thinking that's something that can be trained out of him. How he acted once in that fight is more important to me. During the time that Paul was busy getting to the level of the arena with the Qwardians Ragnar obviously realized that his opponent had better equipment that he did and was adept in using said equipment. Faced with those facts he kept his head both literally and metaphorically, worked out how to deal with his foe's advantages, looked for chances to strike, and then took advantage of one in a big way.
What's important to me is that he showed he's 1) capable of keeping a clear head in the midst of combat, 2) capable of adapting to battlefield situations that are very much not in his favor, and 3) he knows how to create/capitalize on weaknesses shown by his enemy. Those all seem pretty useful for a lantern corps that's being made to pick fights with the Reach.
I think adding in his loss of an arm as some sort of failure of his is reaching a bit; if he'd known about the Qwardians' apparently homicidal reaction to people touching their weapons he likely wouldn't have even grabbed the sword. Because he didn't know about that, because no one bothered to tell him, he did as he would likely do in the fights back on his home planet—kill the enemy, claim a prize, and then mug for the crowd. Also, what? Was he supposed to realize that the Qwardian captain was gonna flip his shit and attack him from left field?
I also think that saying that he's forcing OL to show more than he intended to the Qwardians is a bit silly since his plan is apparently to just start blowing shit up on Qward soon anyway.
Finally, the idea that because there are trillions of people in the universe you can just throw away ring capable candidates seems a bit odd; like sure he can use his memory of the DCU to try to poach folks who might be a fit or go through the ranks of the Controllers' forces for the same but there's no guarantee that they'd actually work—he can make his best (empathy vision enhanced) guess as to whether one person or not will actually be able to use it but it's still a guess.