I would think that Triel is the most charismatic of the three leaders and with her gone the alley bashers and hill folk would pull out. Really once their hidden lair has been found they best leg it.
Iirc the reason for stealing the wands was to ransom them back for money. Once they are found they should go and hide again. This probably means the party will fail to recover enough wands.
This is a disappointing way for the adventure to end so perhaps Tarkilar could stay in the ruins and some of the dead could be brought back to assist him? Skaven can live to fight another day.
I read a more interesting reason for the bad guys wanting the wands which was along the lines that they were using them to drain the water from the ruins to discover something within the lake. I can't recall exactly what it was down there. But if you follow that motivation they might have a reason to stay.