Right now, no, there's no expiration date. CM Skerio confirmed it in the Auditorium when asked this:
What about the shop? I already understood that there will be no more further information regarding other questions but how long it will last the Theon Shop (beginning and ending date)? Free Accounts will be able to access it? Such information is good if we wanna organize our personal schedules...
There is no end date for how long you will be able to exchange Theons. Free accounts can exchange their Theons as well.
Source: Post 39268717
Update May 24th: Theons can now be exchanged for several items with NPC Theodora. According to the news posted today, NPC Theodora and the option to trade Theons for items will remain in the game, so apparently they'll never expire.