Here's everything in Console that relates to Alfred.
5/3/13 11:53:33.517 AM Preview[507]: persistentIdForFileURL: file://localhost/Volumes/Seagate3TB_1/Documents/Setup%20Files/Apps%20-%20Mac/Alfred/key.pdf failed
5/3/13 11:53:33.539 AM Preview[507]: persistentIdForFileURL: file://localhost/Volumes/Seagate3TB_1/Documents/Setup%20Files/Apps%20-%20Mac/Alfred/key.pdf failed
5/3/13 12:07:08.553 PM Alfred 2[172]: [TIMER] 0.376994 seconds to initialise Alfred
5/3/13 12:08:41.875 PM Alfred 2[421]: [TIMER] 0.324301 seconds to initialise Alfred
5/3/13 12:08:55.638 PM Alfred 2[575]: [TIMER] 0.405798 seconds to initialise Alfred
5/3/13 12:09:40.284 PM Alfred 2[176]: [TIMER] 0.415413 seconds to initialise Alfred
5/3/13 12:12:29.090 PM Alfred 2[173]: [TIMER] 0.500356 seconds to initialise Alfred
5/4/13 12:03:06.657 AM Alfred 2[170]: [TIMER] 0.349162 seconds to initialise Alfred
5/4/13 12:05:10.906 AM Alfred 2[174]: [TIMER] 0.438954 seconds to initialise Alfred
5/4/13 12:13:32.538 AM Alfred 2[176]: [TIMER] 0.461078 seconds to initialise Alfred
5/4/13 12:25:38.229 AM Alfred Assistant[504]: Moving Alfred to /Applications
5/4/13 12:25:38.230 AM Alfred Assistant[504]: Looking for instances of Alfred to terminate...
5/4/13 12:25:38.239 AM Alfred Assistant[504]: No Alfred related apps found, great!
5/4/13 12:25:38.240 AM Alfred Assistant[504]: Working with app name 'Alfred 2.app'
5/4/13 12:25:38.340 AM Alfred Assistant[504]: Moving Alfred from '/private/var/folders/yv/9mlk1b3n3bgdc9h25t2cbjnm0000gn/T/TemporaryItems/(A Document Being Saved By Alfred Assistant)/Alfred 2.app' to '/Applications/Alfred 2.app'
5/4/13 12:25:38.341 AM Alfred Assistant[504]: Cleaning up temp folder
5/4/13 12:25:38.341 AM Alfred Assistant[504]: Restarting '/Applications/Alfred 2.app'
5/4/13 12:25:38.614 AM Alfred 2[505]: [TIMER] 0.181526 seconds to initialise Alfred
5/4/13 12:26:57.209 AM Alfred Assistant[530]: Restarting Alfred
5/4/13 12:26:57.210 AM Alfred Assistant[530]: Looking for instances of Alfred to terminate...
5/4/13 12:26:57.218 AM Alfred Assistant[530]: 2 Alfred related apps found, great!
5/4/13 12:26:57.218 AM Alfred Assistant[530]: Attempting to terminate '/Applications/Alfred 2.app'
5/4/13 12:26:57.220 AM Alfred Assistant[530]: Attempting to terminate '/Applications/Alfred 2.app/Contents/Preferences/Alfred Preferences.app'
5/4/13 12:26:57.622 AM Alfred Assistant[530]: Restarting '/Applications/Alfred 2.app'
5/4/13 12:26:58.004 AM Alfred 2[531]: [TIMER] 0.294185 seconds to initialise Alfred
5/4/13 1:52:02.183 AM Alfred 2[173]: [TIMER] 0.410636 seconds to initialise Alfred
5/4/13 1:54:37.510 AM Alfred 2[322]: [TIMER] 0.188703 seconds to initialise Alfred
5/4/13 10:36:13.083 AM loginwindow[62]: Login items - LSOpenApplication returned error -10660, url=/.Trashes/501/Alfred 2 1.54.27 AM.app
5/4/13 10:36:49.717 AM Alfred 2[290]: [TIMER] 0.157384 seconds to initialise Alfred
Yes, I can find almost everything in the Documents or Downloads folder - not everything though. I noticed that there are some times that I can't find. It's strange - there doesn't seem to be a pattern of what files I can or cant find. As for Apps, I haven't tried finding every app, but there a few I can't find (e.g. Textedit). However, I would say that I can find the vast majority of files outside the Dropbox folder.
On the other hand, I can't find a single app in my Dropbox folder - not one.