No, the game cannot be played with the expansion pack alone. Please be aware that you must have a retail version of FINAL FANTASY XIV: A Realm Reborn registered in order to register any expansion pack.
For more information regarding each expansion pack, please reference the URLs below:
FINAL FANTASY XIV: Heavensward
https://na.finalfantasyxiv.com/heavensward/
FINAL FANTASY XIV: Stormblood
http://na.finalfantasyxiv.com/stormblood/FINAL FANTASY XIV: Shadowbringers
https://na.finalfantasyxiv.com/shadowbringers/
FINAL FANTASY XIV: Endwalker
FINAL FANTASY XIV: Dawntrail
FINAL FANTASY XIV: Evercold
Please note, each expansion does not need to be purchased separately. FINAL FANTASY XIV: Evercold includes all prior expansions with the purchase, Dawntrail, Endwalker, Shadowbringers, Stormblood, and Heavensward. A Realm Reborn or the Starter Edition ($19.99 USD) must be purchased and registered separately before Evercold can be registered. Alternatively, the Complete Edition of FINAL FANTASY XIV ($59.99 USD) can be purchased, which will include A Realm Reborn and all currently released expansions. Please also note that the Collector's Edition of Evercold does not include A Realm Reborn.