Hmmm... Yah, a file that is not closed properly cause someone just yanked the power cord out of the PC to haul it through the broken window isn't a useful file anyway...
I am thinking you need a 'Teddy Bear' camera, or a 'Clock Camera' or 'Book Camera'...
If the concern is a physical breach and theft of the computer... then you really should go with multiple secondary cameras.
Even if the file started uploading immediately, it's not going to be properly closed and most likely isn't recoverable... and Internet file transfer is slow depending on the day, the angle of the sun... many factors can slow it down.
Hit the SpyShop and pickup some secondary cameras that look like ordinary cheap stuff no one wants to buy... they take SD cards and should be relatively inexpensive.
Okay - They aren't inexpensive...
http://www.uspystore.com/hidden-cameras.html
But at least they may stick around to reveal the thieves!
HTH...
Patrick