Ladies bike on a car rack
It depends on the exact size. To figure it out, you'd need some detailed measurements. If it fits, there's really no problem.

It's more likely a problem with a "ladies" (low top tube) bike if it's smallest size and/or if the frame is sized for a suspension fork.

Look at the picture of the bike. See how the distance between the top tube and the down tube is quite narrow up by the head tube? It's possible that with the smaller sizes of this bike, there isn't enough room to fit both of the bike rack's posts inside that triangle.

However, that bike comes in 3 different sizes. The bigger sizes have a longer head tube and a longer top tube, so there's more room.

If the bike fits on the rack without that "beam" bar, there's really no significant problem. There won't be any rack stability issues, since the weight of the bike really doesn't change much with that tilt. The handlebars probably won't tilt far enough to hit anything. It's possible that it will interfere with fitting 3 bikes on the rack, since the rear wheel will be up where the bike next to it's handlebars need to go.