It will still be able to operate on the Met Main between Harrow platform 2 and Amersham (only), and indeed this is generally accepted to be the plan for future heritage operations, including Sarah Siddons. The difficulty will be transferring the trains to and from that part of the Met.
Both the 1938 stock and Sarah (and the Q stock) have been costed for CBTC, but it is extremely unlikely that this will come to fruition on funding grounds.
There is capacity to operate the '38 stock on the Picc and this is most likely due to there being easy access from Ealing Common. Movements onto the Bakerloo will require arduous engineering hours transfers, and would be far more complicated than a transfer onto the Met (indeed, you'd have to transit via the Met...). Capacity on the Bakerloo is very tight down towards Elephant also.
All that said: the only accurate answer at the moment is "no-one knows". CBTC is running later and later, and until the first section goes live and settles down the possibilities are literally endless.