I can't think of anything prohibiting them from doing so.Does a Fragmented BG pursue routers? They can't charge but I can't see anything to prevent them pursuing.
Possibly, but we are trying to stick to a KISS principle, on which count this probably fails the test.Would it be a nice touch to allow a Fragged BG to recover to Disp if all of its opponents rout?
If you would like a rationalisation: Yes their morale might be improved, but several of their officers have probably been killed, they are shell-shocked and disorganised, until a dashing fellow on a white horse rides up and puts them back in order.