Cool! I just found a way to do this in TB2 - and just confirmed it also works for TB3b4 - by simply editing a preference in about:config...
Preference is: mail.addr_book.quicksearchquery.format
All I did was change the original/default:
?(or(PrimaryEmail,c,@V)(DisplayName,c,@V)(FirstName,c,@V)(LastName,c,@V))
to
?(or(Company,c,@V)(PrimaryEmail,c,@V)(DisplayName,c,@V)(FirstName,c,@V)(LastName,c,@V))
This doesn't change the hint text in the Quicksearch box (it still only shows 'Name or EMail'). but it definitely searches the Organization. yay!
Peeve: the field NAME (in the code) is 'Company' - I hate discrepancies like this, why didn't they just use 'Company' for the field LABEL too??...