Probably not, since it doesn't appear that Allshare throws numbered errors, so looking up the error is a matter of typing it into a search engine and reading any hit that seems appropriate. Things like "unable to download" or "unable to update" - if you do find any sites mentioning the error - would be useless, because those messages are about as helpful as "there's been an error". (An error without a solution should never be shown to the user of any software or firmware. It's sloppy, careless programming, at best.)
As for "Samsung tech support", that's not a department, it's a joke - there isn't one for most problems. If it's under warranty they replace it (and if it's a phone, it might be with one that's been water damaged), but if it's "can't update the firmware", they have less of a clue than you have. (The problem could be as simple as a "hardwired" IP address for updating burned into the device - and if it's changed, it means "no more updates".)