The Russians would have had to launch 3 or 4 (if an unmanned Soyuz launch is impossible) Soyuz within 30 days. This assumes they had 3-4 Soyuz rockets lying around at the launch site, finished and ready-to-launch.
Using a Proton wouldn't be feasible; it's never been used to launch Soyuz capsules so they'd have to manufacture a payload adapter.
The Soyuz could only be launched unmanned if its software were able to do automated rendezvous and stationkeeping, AND if its airlock were able to be opened from the outside.
The same constraints apply that TFA talked about: preparing 1-3 missions at a hugely compressed time schedule.
You also have the additional problem of having 4-5 spaceships flying in close formation, each in a slightly different orbit. That's a bad enough problem with 2 ships, but with 4-5 you need all of them to be manned to avoid collisions and blasting EVA crew with rocket exhaust.