Yes, EA is supposed work this way, and, it sorta does. It is basically supposed to replace the lock screen with the EA screen and it has it's own slider unlock feature. But, once your Security Lock Timer goes off and you'd have to enter your pin, pattern, etc. you now have to unlock EA to get to your regular unlock screen, then unlock that, then enter in your pin, pattern, etc.
I emailed them about this probably three months ago and they had some reason why it wasn't working properly and made it sound like it was never going to work properly. I just checked it out now and it's still not working. It would have been a great feature. I still use EA for my email, calendar, tasks, etc. but that one feature just doesn't work right.