I'm Going on a Vacation, Can I Get Invisalign There Since It's Cheaper?

I would say with some things it is ok to have them done some place where it will cost less. Crowns, bridges, root canals, all can be done somewhere else with little problem as long as they are done correctly. Something to consider when dealing in locally is reputation. Not only is it easier to check on someone's reputation, but if you have trouble later, they are more likely to work hard to keep you happy because they want to maintain a good reputation.
With Invisalign you will need to show up to the dentist office at 6 week intervals anywhere from 5-10 times. So I wouldn't recommend that unless you will be there on vacation almost every month. Also you may need something done in between those appointments so it could be very difficult to do. If you want veneers, I have had people travel from great distances to get them done. Wouldn't recommend that with braces.

It's not the type of treatment that is a one appointment kinda thing. Of course, I wouldn't travel to mexico for a nose job and yet thousands of americans do just that.
When it comes to healthcare, always remember that there is always a chance that you would need follow up care then you would need to travel again. Invisalign is a monthly committment and thus needs constant monitoring.

In average, it takes 3 weeks for Invisalign to create the 3D plan and another 5 weeks to create the aligners. Normally, treatment requires visits to the dentist or orthodontist every 6 weeks and treatment lasts an average of 11 months. I suppose if your vacation is REALLY long.