The Stuka isn't a STOL plane like the Storch, you'd probably end up crashing it on take off with the long roll out for take off out of a V base.
ack-ack
Actually it pretty much was a STOL aircraft. The prototype was capable of taking off in about 800ft with a 250kg bomb using the 600hp Jumo 210 which was always said to be greatly underpowered with a Tow of 7300lbs. By the time they developed the G model, the engine had been changed multiple times and was now outputting over 1400hp. The frame itself had only gained About 2900lbs in empty weight(including guns but excluding ammo/bombs), to 7900lbs, over the A model, but it was powered by an engine putting out over twice the power.
So either way, the G model modestly loaded could take off in 800ft or less. It's not like we have the 1000kg bomb on it, which it did carry IRL.
And besides, there is plenty of room for it to take off within the current base's footprint.