Transaction log in the full backup
The simple answer is yes, it will contain the transaction.  Also simply the backup contains anything that happens before the end of the backup, not as of the start.  The full backup actually contains the transaction log information as of the completion of the backup.  When  you do your restore any transactions that were not committed at that time get rolled back.

If you want to learn more about it you can research backup internals.

Here is a technet article on it and the Kin's answer to this question has a number of additional good links.