A few of my bettas have gone for 2 weeks without eating. Not by design or negligence, but they were adapting to their new surroundings. However, they would never be survivors if they expired after 1 week without feeding them. What's more important is to keep the water clean.
As long as a Betta is well fed beforehand, going a week without food will be fine. They often do this during spawning, so no reason he couldn't while you're on vacation. I would be more concerned about the water change that would be needed for a 2 gallon tank, going a week without a water change is a bit long unless it's filtered (I don't think you said if it is or not).
Bettatalk is good information, but also read other stuff, she does have some questionable information. She's not the end all, be all of Bettas (although she'd like you to think she is). <this is my opinion and does not necessarily reflect the opinions of the forum owners or of others on the forum> hehe
It's filtered. I would give it a good cleaning before I left anyway, just to be sure. I really appreciate everyone's advice. I just read bettatalk's site it's very interesting. I must have a very low betta though because he eats flake and pellets without complaint. But he does snap up dry bloodworms