I don't think this will fly. When you installed Autocad the first time, you gave the product number. This was mixed with information about the PC on which you were installing. The resultant combination becomes an "installation ID."
When/if you try to install on another computer, the information about the PC will not match. You may be able to install, but will shortly be advised to purchase or lose it.
I base this opinion on something I read regarding WinXP:
When you buy Windows XP in a shrink-wrapped box, you are allowed to install one copy on one PC. When Windows comes pre-installed on a new PC, it stays with the PC. You cannot transfer it from the bundled machine to a different machine. MS uses a technique called "BIOS locking" to make sure the copy stays ties to that specific PC forever.
Windows installer makes you type the 25-character code that's printed on the case. The Product Activation program looks at various serial numbers inside your PC - the processor, network card, disk drives, etc. - mixes them together, and produces a second 25 character code that identifies your PC. These 50 characters, together, are called the Installation ID.
When you activate XP, you give MS the 50-character Installaton ID. If nobody else activated that 25-character code or if it has been activated with that specific Installation ID (which means you activated this particular copy of XP from the same PC twice) MS send back a 42-character Confirmation ID. The Installation ID and the Confirmation ID are stored on our PC.
If that 25-character code has been already been used on a different PC you will be notified that the number of times you can activate Windows with this product key has been exceeded.