I've successfully purchased tickets from the Chiltern website and loaded them onto my Chiltern smartcard from their app for Greater Anglia-operated services.
The barriers at one end were totally fine with this. At the other end (Stansted Airport) I told the staff my ticket was on a smartcard and they just waved me through with no further checks.
I've even had a smartcard ticket on a Chiltern smartcard purchased from Chiltern, on a flow operated by Greater Anglia, checked on a CrossCountry train - and everything went surprisingly smoothly.
While the Chiltern site says that any operator's smartcard can be used there, it's not currently working. I emailed them about it and apparently they're only accepting Chiltern smartcards for now, but it should work with other operators cards in the not too distant future.
While I haven't checked too many corner cases of these kind of tickets, I've had a pretty good experience with the scant few non-season tickets that are enabled at the moment.