The answer is no. There is no alignment of axes.
The plane of the solar system is TILTED 60 degrees from the plane of the Galaxy.
I don't know much definite about the orientation of other planet systems. But from what I've read nobody EXPECTS them to have their axes aligned in any special direction. The expectation seems to be that it's basically random.
Also the SENSE of the rotation is not necessarily consistent.
Roughly speaking the Solar System N pole (instead of point straight out of the plane of the galaxy, perpendicular "up") is tilted 60 degrees towards the direction that the Sun and her planets are going.
Now the sense in which the Sun and most of the planets are rotating follows a RIGHT HAND FIST rule, with your thumb in the N pole direction. If you look down on your thumb the fingers are going counterclockwise and that is how the Earth is rotating and also how the Earth is orbiting, and the sun is rotating, etc.
But if you tried to align the solarsystem with the galaxy by tilting the solarsystem axis 60 degrees back upright, you would find that even though the axes were parallel the galaxy would be revolving according to a LEFT HAND fist rule. If some aliens would take you on their ship far far above the Earth's north pole and you looked back you would see most of the stuff in the solar system rotating and orbiting counterclockwise, but you would see the sun and other stars orbiting the galactic center CLOCKWISE.
So there is a strong inconsistency. One has to suspect it's random uncorrelated except for nearby things.