I needed to have separate (different) settings for sync settings for different accounts (sync on WiFi only vs sync on WiFi+mobile connection).
But there is no account level option for "scheduled checks on WiFi only", sorry.
Kostya, I am curious: there are many per-account options ranging from checking e-mail to some extremely cosmetic ones (appearance, colors, etc.). But there is no per-account option for this functional option.
Use case: one account is "important" (say, business, or close family), and the rest of the accounts are not as important. So, one wants to receive updates while on the road for the first one, and not for half a dozen others (to save the battery, mobile data, minimize interference with the navigation apps, ..)
PS. I am not using tasker.