Will Shroud of the Avatar feature single-player gameplay?

Yes, absolutely!

Can it be played purely offline, or is online a requirement?

Either is possible, depending on your preference.

Portalarium on Shroud of the Avatar’s multiplayer modes:

Here are the ways we anticipate the game can be played:

Single player offline:
This is the DRM free, completely off-line version of the game. Your character is stored on your computer and can not be used in any of the online modes.

Single Player Online (SPO)
In the SPO mode you connect to the server, receive content updates, and can see the long term changes others are having on the world. However, you are not visible on anyone else’s screen, nor for grouping, and you don’t see anyone else in the world. You can switch from SPO to FPO or OPO modes whenever you like while in a city or overland map. Some parts of the main storyline quests may temporarily force the player into SPO mode for some parts of the quest.

For more information, see this video: