At the Eastern end it'll be fine to begin with. 315s doubled up will take about 1000 people tops versus 1500 on a 9-car 345. Then consider that 12tph is a lot better than what you currently get - at present, select stations like Ilford, Romford and Gidea Park get 14tph versus the 16 they'll get with Crossrail, but Harold Wood and Brentwood only currently get 8tph in the peak rather than 12, so for some stations it's a 50% frequency increase and a 50% capacity-per-train increase.
The Western end should be covered by the considerable increase in capacity from 165s to 345s. Really it's only the core section that's in any doubt for meeting the capacity requirement. It'll take a fair bit of load off the Central line for passengers using Liverpool Street, Bond Street, Tottenham Court Road and Farringdon instead of Chancery Lane, as well as a small handful who'd be willing to use Bond Street or TCR as an alternative to places like Oxford Circus and Marble Arch off the back of getting less cramped trains. It'll also take load off the North Circle for Whitechapel to Farringdon inclusive and Paddington, as well as reroute all sorts of other two-stage journeys like, for example, Canary Wharf to Willesden Junction routing people off the Jubilee Line. It'll also be taking some demand off the DLR from journeys to/from Custom House and Woolwich to Central London. Trains will be less horrifically crowded outside Central London during peak hours but I can easily envisage the core section in Zone 1 being pretty much 'full' from within a month of the system opening once everybody who uses the tube regularly has worked out how best to route their journey.
As an example, in the evening peak it may even be viable for people travelling to stations covered by the Gidea Park stoppers (e.g. Romford) from, say, Farringdon, to board an Abbey Wood service, which I imagine will be quite a lot less crowded in that direction, and change at Liverpool Street onto the high-level terminus to board a quieter train and get a seat the rest of the way, who knows. It'll certainly be something fun to experiment with.
One thing's for sure, if I'm still working near Farringdon when the core opens at the end of the year, I'll definitely switch to using a 345 to get to Liverpool Street rather than the surface lines. They may be a lot more comfortable than the Central line, but punctuality is pretty mediocre to say the least.
