Sure but there are star systems that are above and below the exact ecliptic of the galactic plane. We're not on the ecliptic that's why you can't see the milky way as well in the southern hemisphere because we're kind of below it.

If a ship was travelling from Sol to Arcturus it would travel up (relative to the galactic plane) because we're slightly below it and it's considerably above it. The galaxy is very thin compared to its width, but it's still of thousands of light years high.