Crossrail Information Paper E2 relating to cycle carriage suggests that bicycles would be banned at all times between Abbey Wood and Acton Main Line - i.e. the [deep] tunnel sections.
Of course cycle carriage outside peak hours is possible on the DLR beneath the Thames in, er, deep tunnels.
It seems to me that the probable banning of cycles on the Elizabeth may relate to access to the platforms. But again, this is no problem on the DLR, and indeed wheelchairs and buggies will be allowed, I suspect, on all sections of the Elizabeth.
I suspect the carriage of unfolded cycles in the central area would generally be between stations outside the central tunnel area. One does wonder how crowded the trains will be in that section.