Maybe for a short period of time you could move, but you could not cruise around with such a small crew for any length with a large complex rig. The need for large numbers of crew on these sort of multi masted ships comes from the need to furl and unfurled sails as well as adjusting the angle of all the yards holding them. This is required not just to control the speed of the ship, but the ability of the ship to sail close to the wind, in the event the wind is not blowing directly in the direction you wish to go, and vitally, to maintain course and stability in adverse weather.

With only six people you've got 1 man on the helm and 5 people probably couldn't furl even one large sail at a time, let alone do anything else. If the wind shifted suddenly the ship would be in an incredibly dangerous situation and could capsize before you could reduce the amount of sail you had set. This was something that needed constant adjustment.

Imagine a car going down a twisted mountain road with no brakes. Now imagine if you wanted to apply the brakes on the car you physically had to take each wheel hub apart and put in a different brake rotor each time.

That's a sailing ship with a rig like this and insufficient crew is like.

If you wanted to sail with a very small crew you needed a simpler rig, like a schooner rig or just a couple lateen sails. Then you can control them more easily. The downside is this is much slower when the wind is favorable. Sailing a big ship with a tiny crew across and ocean is very plausible, but it must be a suitable ship design. Anything resembling a real Galleon is not.

By the late 19th century though people were building the final generation of wind jammers with steam donkey engines on deck, and that allowed some huge six and seven masted fully ship rigged vessels with huge numbers of sails to operate with small crews. But small was still 40-50 people.