The rebels [could / were able to] draw on the support of over 20,000 soldiers
Solution 1:
Let's say the rebels had convinced 20k soldiers that their cause was a noble one but told them to not say anything and just continue to pretend to be loyal soldiers. In this case, the rebels could draw on the support of over 20,000 soldiers, but choose not to.
Later, perhaps, during a battle which they were losing, the rebels were able to draw on the support of over 20,000 soldiers and thus emerged victorious.