I am a frequent (although not compulsive) user of Twitter.
I have my favourite client on my Mac and my iPhone.
One thing that I believe DevonThink would be exceptionally good for is archiving tweets. I suggest this could be a background feature where DevonThink could dowload tweets on a repetative basis that is configurable.
What tweets are downloaded could also be configurable (only my tweets, only the tweets of those I follow, all tweets by mee or those I follow).
For me, this would be a fantastic addition to DevonThink, particularly as version 2 allows multiple databases so I could devote one to this function.