If a split test is done on a page with Google Experiments and a visitor returns to make a purchase 3 days later through an email, will the variant that the user first saw get credit for the transaction?
If they are using the same device, probably yes.
With Google Experiments, if they should see the same version of a page, and also be recorded as having used that version for getting credit for the transaction.
If they are using different devices, may be. For example they browsed on your site on their mobile, and then went back and used a desktop to purchase.
What Google has done, is upgrade Google Analytics to something called Universal Analytics, where Google attempts to follow users across platforms.
This above assumes, that the transaction tracking is set up correctly within Google Analytics (a big if, analytics set up can be tricky for many E-Commerce set up and will require help of a programmer).
Their are other programs, paid, which may be a better choice for doing Conversion Optimization. The two most popular ones are Visual Website Optimizer and optimizely.
And when doing testing, remember, document your tests and run them long enough so you get statistically significant results.
3 conversions on variable A, and 1 conversion on variable B over a holiday weekend is probably not representative enough to make changes to your site on. And even at 95%, that says there is a 1 in 20 chance your wrong! So run your test long enough, so for example, you are not getting only Saturday type traffic.
Good luck with your testing!