Dropbox won't upload when the computer is asleep.
All uploads and downloads fail or stop when your computer is asleep.
So you must make sure your computer stays awake when uploading or downloading files to Dropbox or downloading or uploading any other files as well.
Under a Windows OS, 'sleep' means that the computer is off and not running programs, but memory is being held live so that it can wake up very quickly.
In this state, NO, dropbox can't sync, because it's not running.
Your computer does not still upload when in sleep mode.
Uploads will be interrupted and fail if your PC goes into sleep mode during upload.
When your computer goes into sleep mode it stops activity such as uploads, downloads and internet connections.
So if you need to keep your computer on to upload files or download files then you can set the laptops screen to go off but still keep the computer on and out of sleep mode.
With a desktop you could just leave the computer on and shut down your computer monitor.
The application will resume uploads even if you shut down during a sync operation.
Files sent there will upload as Internet is connected.
If however you do so from a browser this may not be the case.
Some systems may view this the upload as activity and thus not sleep until the upload is complete.