Is it legal to download software from a 3rd party site if you intend to register and activate it using a legally purchased serial number?

Recently I lost some software CDs, but I still have the serial numbers. These serial numbers are registered to my name from when I purchased the software legally.

Would it be legal to download the unregistered and deactivated software from a 3rd party site and then proceed to install, register and activate it on my personal computer, with my personal and legal serial numbers, for my personal use?

Why / why not?

Thanks!