I think it will vary by person, and that is because as [MENTION=14857]labyrinthine[/MENTION] mentioned, there can be different underlying things leading to boredom from one person to the next. I think the same goes for other emotions, where one person may put out great work when feeling that, another person might not be able to do so at all.
I know many people cite that negative moods/being in a bad place can foster good creations. For me it's totally the opposite. My best work is when I am feeling positive and inspired, and have a desire to create something beautiful -- and with that comes a vision and intuitive ability to execute.
For me, boredom goes hand in hand with feeling blah and uninspired about things. Thus I'm not going to be able to create anything I like. I'll sometimes try painting when bored, just because, well, I'm bored, and so I try to force myself to paint. I'm pretty much never satisfied with it, and usually stop quite soon after trying/starting, because my heart's just not in it and ultimately I don't feel like doing it (I'm just 'trying' to do it). ie if I felt like doing it / felt inspired, I wouldn't be bored.
The best I can hope for when being bored and attempting to create something is to just treat it as practice - practice, experiment, know nothing amazing is going to result from any of it.