I am scanning a lot of photos. In this process I am embedding a date in the filename. For example "2006_05_13_Italy_Sandy_Tom_Rachel_Brian". Is it possible for A Better Finder Attributes to pick up this date that is in the filename and change the creation date of the file to that date?
We wouldn't know anything about "A Better Finder Attributes". I'm not sure why you are asking about it on the Exiftool website. You would have to ask the author of that program.
Using exiftool, the standard embedded time stamps require a time as well as a date. The de facto standard for that is to use "00:00:00" as the time.
As long as there are no other numbers in the filename, then you could use this command, based upon FAQ #5 (https://exiftool.org/faq.html#Q5)
exiftool "-AllDates<$Basename 00:00:00" /path/to/files/