The alternative route suggested on the poster on the subway is via the south circular, but it does add a few minutes to a walk round. Accessing the station will still be possible from either side but it does not look like crossing over the railway will be allowed via the two sets of ticket barriers.
Although the poster says it may be closed for six months this is a maximum expectation for the time taken to complete the work, and it is more likely to take 3 months. Previously the contractor have said that the underpass would remain open for the whole time work was happening (which always seemed unlikely), but I think there is still the possibility that they will keep it open when safe to do so, even while work is going on. But with the lighting being replaced and new roofing being put in place there are plenty of safety issues to consider.
A lot of this is speculation on my part as the council have not responded to any of my emails on the subject. But the most important thing is that the work will start very soon.