Don't count on it. I have the same problem, tried the support route and they've been spectacularly unhelpful.
For example:
"If you bought this on the day of release, the serial key should be on the back of the manual or on the inside of the box (perhaps below the DVD itself). You have to understand that, without a serial key as proof, we cannot offer a voucher for D2 DC."
And
"As I stated in the previous mail, without a serial key, we cannot offer the upgrade to Divinity 2: Developer's Cut.
I apologize for any inconvenience."
As a longtime Larian fan I am very disappointed in them. They could take some tips from CD Project on how to treat their customers.
