Application to automatically find related documents on your entire Mac?
This will be extraordinarily difficult to do at run-time, and with any document.  The few solutions that have implemented this technology (remembrance agent http://www.remem.org/ and Dashboard http://nat.org/dashboard/ are probably the most notable and "successful") required specific search indexers for each type of application and up-front document analysis.  (Very much how you can't search in Spotlight while it is "updating".)

For example, if you typed the word "from", you would not necessarily want to see all of your email messages just because they all feature the word as part of their metadata.  However, if you typed "Art Taylor", you would expect to see email, chat, and other documents related to me.

The problem is of summarizing the semantic content from the structural content.  That's why DEVONthink requires you to import the documents.  It can summarize the documents and present results more or less in real time, because it has done the summarization up front.  Spotlight does some of this as well, but no great context aware knowledge and memory augmentation applications have popped up that offer universal document support.

If you google "knowledge augmentation", you will find a large number of articles and papers on the topic.  People are very interested in this and I think it is just a matter of time before someone attacks the problem with a commercial solution.  Gordon Bell had a tantalizing project called "MyLifeBits" http://research.microsoft.com/en-us/projects/mylifebits/ that was a little over the top, but IBM http://www-03.ibm.com/press/us/en/pressrelease/24750.wss is doing some research on associative recall.  Note the "Capture" and "Ingest" stages.  The scope of both of these is much beyond simple document relationships.

Years ago, I tried the DEVONthink "put it all in there" approach, and as you probably suspect, it was a disaster.

Best of luck.