No, you won't have to plunk down some cash to play the Anthem demo before the game's February 22nd debut. BioWare and EA have announced that the sneak peek on February 1st through February 3rd is an open demo that will be accessible to anyone on PC, PS4 and Xbox One. If you've either pre-ordered the game or subscribe to Origin Access, you'll just play earlier -- a "VIP" demo will run between January 25th and January 27th. You'll also receive an in-game item to flaunt your early adopter status.
This isn't the same as Destiny's public alpha and beta releases, which were as much about ironing out pre-launch bugs as anything else. However, it does serve a similar purpose in acclimating gamers to a shared-world shooter. BioWare needs a healthy player base if Anthem is going to fulfill its promise of a social gaming experience, and that means attracting as many people as possible -- particularly those who'd otherwise never have considered playing in the first place.