I don't think this is true about all drivers needing to be trained before entering service; they started appearing on Manchester-Llandudno services before all of the traincrew at Chester had been trained up. After 6 months of training (which will be around July) you'd expect a sizeable number of drivers and guards to have been trained up across all the depots and probably enough to cover a diagram.
I think other TOCs have links which sign particular units so they could do this with the 197s while training is ongoing. Also possibly have training runs on diagrams in passenger service.
It's not so much that every driver has to be trained, but the complexities of the Manchester - South Wales service is such that it does need to be a large enough group of drivers at all 4 depots (Crewe, Shrewsbury, Cardiff Mainline and Carmarthen) before introduction can take place.
TfW do occasionally allocate certain traction only to certain links, and I believe there's currently only one link at Cardiff Mainline getting trained, but it's a very complex and difficult thing to set up - especially when the reality is all drivers at the depots concerned need training ASAP.
At the moment there's very limited work for these units on routes that the other depots sign, making training on service trains a little more difficult (though not impossible) - but that should hopefully be changing soon when they start appearing on Holyhead - Cardiff services.