You probably would've needed to get an address there somehow, yes. There's services that do that for you, the non-shady ones being provided by lawyers and notaries.

[ed.: a tiny office in Leipzig is pretty cheap too, but you'd need to ensure mail doesn't pile up there unchecked.]

Unfortunately I'm not joking about this entire thing. Berlin's underfunded, overstressed bureaucracy is to be avoided like the plague.

[ed.2: to be clear, it'll still not be great. Just less bad.]