AppleSeed is an invitation only program where customers are selected by Apple to participate in voluntary testing of new software. So, no, you can't register or submit your name into a pool of applicants. (I've checked the FAQs just to be sure.)
"Apple Software Customer Seeding is a program where customers are invited to test pre-release software products in order to provide Apple Software Engineering with real-world quality and usability feedback."Once you have been accepted into the software testing program, you are "strongly [urged] to test the software and [we] require your feedback. A variety of reporting tools are offered providing engineering with functional data. Failure to actively participate may disqualify you from future seeding programs." In other words, Apple expects you to work hard for your exclusive access to software that is still under development.
Back in the heady days of Palm, in all of it's variations, I was a vocal advocate in both public and private forms to urge Palm to setup such a program as a means to help squash software bugs in the Palm OS, and later, webOS software. I'm glad to see that Apple has setup a program like AppleSeed, even if I'm not contributing to it.
To learn more about AppleSeed, check out the Apple website.