It's an interesting idea and the technology and design are really, really good. It's also not your typical Twitter aggregator: all the Tweets have permalinks going to the Tweeji domain itself and you can sign in with your Twitter account to follow, reply and the rest.
So rather than just gathering Tweets, Tweeji is a kind of self-contained "mini Twitter" of its own - it'll be interesting to see whether this awesome software is reused for other purposes in the future. And if you find an interesting Twitter user posting posthumously, you can also contact Tweeji to have them added.
Where it falls down, however, is in the branding. There's just something distasteful about "following dead people" - a morbid marketing angle that leaves an unpleasant taste in the mouth. If the angle was more like the wonderful Historical Tweets, which humorously creates faux tweets from historical figures, it would be great. It's simply the case that wallowing in morbidity doesn't appeal.