Might want to pose your Vespa questions over on modernvespa.com.
I had the earlier Vespa GTS 250ie. A very high-quality and (relatively) powerful machine (I took it regularly on the superslab with no problems), but not - for me - an off-road/gravel scoot, though I did some trails on it; others have different experiences, including some really epic trips in undeveloped areas, low clearance notwithstanding.
Modern Vespas are (again, relatively) heavy and complex. You may not be happy getting gravel dings in the steel monocoque body work. They're also expensive - in the mid-Atlantic states and hereabouts, you can count on adding about 19% to the MSRP once tax, fees, freight, title & reg, etc, have been added in to get it out-the-door. With added-on racks, topcase, Stebel horn, & assorted other farkles, I had well over eight grand in mine. "Used" might be a cost-effective way to go. YMMV.
They are cool, though; if the appeal is there for ya, why not? Any bike can be an adventure bike.
DR-Z400SM, '68 Honda 305, '64 Honda C110, '06 Honda VT750, GTS 250ie, Genuine 150, Vino 125, Zuma 125, Yam C3, Honda Met, Tomos ST, PCX 150, Honda PS250 Big Ruck, Vino Classic 49, Honda Rebel, and a Lifan CT 70 clone I forgot about...