It is possible that Joey actually converted before she left Tyrol. I am not sure when her religion is mentioned in the earlier part of Exile.
She hadn't converted before they went to Guernsey. Here's the relevant passage from the cut chapter (from Faded Page):
‘Joey!’
‘Jack! At last! What an age you’ve been. I thought the Gestapo must have got you this time. Where have you been?’
‘To see about our wedding, my child. And I’ve come to the conclusion that we’d better wait till we get to England for it. There’s so much red tape over being married out here, especially as we are of different religions, that I felt we’d far better leave it till we get to our own country. Besides, if we do that, you’ll be able to have some of your own people with you.’
Joey sat up in the hammock in which she had been lounging, and, as a natural result, rolled out on to the grass.
‘Hammocks may be very comfy, but they are the limit,’ she declared, as she rubbed an elbow ruefully. ‘Jack, what did you mean?’
‘Just that I’ve heard from the Sonnalpe today. Madge left last Thursday, bound for Guernsey, and Margot and the babies. The Government is taking over the San, and Jem is following her as soon as possible.’
Then there's a whole lot about how all the others who fled from Austria with them have gone to their various homes, and how Jack and Jo and the Robin and Miss Wilson will travel to Guernsey. Then it continues with Jack saying
You ought to be with Margot and Madge and the babies—let’s see; this is Tuesday—well, Friday or Saturday at latest. Then, I suppose, we’ll have to wait a week or two before we can be married.
Then there's more chat about whether they can do the journey more quickly, then we move to Miss Wilson and preparations for the journey and departure.
I suppose her actual conversion and acceptance into the Catholic church must have happened in the ten month gap that follows.