Technically, no. That would require that they log in under your Battle.net account, and that's against the Terms of Use.
Emphasis mine:
Username and Password
During the Account creation process, you may be required to select a unique username and/or a password (collectively referred to hereunder as "Login Information"), and you may not share the Account or the Login Information with anyone other than as expressly set forth herein. You are responsible for maintaining the confidentiality of the Login Information, and you will be responsible for all uses of the Login Information, including purchases, whether or not authorized by you. In the event you become aware of or reasonably suspect any breach of security, including without limitation any loss, theft, or unauthorized disclosure of the Login Information, you must immediately notify Blizzard by emailing wowaccountadmin@blizzard.com.
It does appear, however, that you could transfer the license, although it is not guaranteed:
Game Transfers.
The Authentication Key that accompanies most Game clients can only be used once, and will connect a Game license to the Account under which it is registered. The transferability of your license to a Game client is governed by the Game EULA; provided, however, that any transfer of the Game client shall have no impact on the Account registered to you, and that Account shall not transfer with the Game client. Purchasers of a license to a used Game client must follow the process detailed on the www.Blizzard.com website, which may require payment of a processing fee.
More specifically, the StarCraft 2 EULA, mentions that transfers are generally prohibited. However, if you're in a jurisdiction where transfer is allowed, they do have a process for it:
No Transfer or Sublicense.
THE GAME IS LICENSED, NOT SOLD. NEITHER THE GAME NOR THE LICENSE GRANTED IN SECTION 1 MAY BE SUBLICENSED OR TRANSFERRED TO ANY OTHER PERSON OR ENTITY, AND ANY ATTEMPT TO DO SO SHALL BE NULL AND VOID. If a court of competent jurisdiction finds the foregoing sentence to be unenforceable, you agree that you will call Blizzard Customer Service at 1-800-592-5499 to arrange for the transfer of your rights under this Agreement to another person with a valid Battle.net account; provided, however, that Blizzard may charge a processing/handling fee to facilitate the transfer, issue a unique key to the transferee, and remove the preexisting key from the Battle.net account registered to you.
