TfL will publish a "response to consultation" in June. This will probably be a fairly boring document not of much interest. The next real event will be in late summer (October perhaps) when a new consultation is expected. It is likely that consultation will have TfL's "final" preferred route choice.
If the preferred route choice is Balham, then it may or may not imply a shaft on the common - ie. it is possible that TfL may find a way to route Crossrail via Balham without a shaft on the common (but there would be a shaft somewhere else).
If the preferred route choice is Tooting Broadway, then it is expected that the shaft will be on car parks near the prison, not the common.
If the preferred route is Earlsfield, then there would be no tunnelling anywhere near the common.