It absolutely does. Because they won't give you another job to do until you complete it. That was like 20 or so levels ago so if I get a chance I'll go back tonight and see if it's still the case. I also looked this bug up online and it definately exists. But like I said, I'll check it out next time I play. It didn't work 10 levels later but that's the last time I checked.
You are right! If you already have a quest in your log from one of the companions to intimidate someone who no longer exists, then you won't be able to get another radient quest from a different member of the companions because they will tell you you are already doing work for so and so. If that is the case then, yeah, you are hosed.
Unless, of course, you have a save from prior to the time you took the intimidation quest. If you did, you could reload that save and go talk with a different member of the companions for work and hopefully get a different radient quest. There are something like seven different radient quests available and you only have to do one of them to advance the questline. But I hear you on not wanting to replay several hours, or in your case 20 levels.
I got lucky when the companions questline bugged out on me. I had a manual save from an hour before, so I did not have to redo much and the bug was immediately obvious, so I stopped, checked the UESP and other online sources for the solution and proceeded from there.