Yes, you can do it in several ways. First you can specify the script int he users properties in ADUC. I don't recommend this however.
Ideally I would simply set this up like any other login script using a GPO. Edit the GPO security and remove the Apply next to Authenticated Users. Then add your specific user and select to Apply to that user.
That will handle your question, but I would suggest you step back and maybe rethink things.
Do you already have a login script? If so, why can't you add the specific code you need to execute for this unique user to the exisiting script? Take a look at my FAQ on login scripts. You will see that you could make this user a member of a specific group and execute that code as needed. faq329-5798
I hope you find this post helpful.
Regards,
Mark