No! Purchase is not necessary to play Heart's Fortune; it is optional.

In the shop, there is a Fortune Hearts event bundle, which will offer you 70 free tickets upon its successful purchase. Purchase of this bundle will award you 70 free tickets. You will be awarded these free tickets with the first purchase of this bundle within a 4-hour window. There is no cap on purchase of the bundle but free tickets will be awarded twice in a given 4 hour window. Only after the current 4-hour window expires, this limit resets and your next purchase will again grant you free tickets in the new window.