Yea, it's normal, but probably not good.
I try not to move my laptop when the hard drive is running... just not a good idea.
Think of it this way. There is a 7200RPM hard drive running in my laptop. Your's, I don't know the speed.
Anyway, that 7200RPM hard drive spins 120 times per second. Basically, a gyro of all my data spinning around 120 times a second. Gyro's don't like to change direction except in the Z direction (vertically), so I can only imagine that some warping and bending (very slightly) of the disks occurs when moving it in the X, Y, and Z axes simultaneously, and it's bad when the heads of the armature touch the disk. They're supposed to just glide right above the surface, but when you move it, and it doesn't click, then it can lead to bad things. On top of this, I'm sure there is a chance of the armature moving around if you move it horizontally, causing data corruption because it's writing to the wrong part of the disk.
Wonder why laptop hard drives fail more than desktop hard drives? They are moved around more.
So yea, it's normal, and no, it's probably not good. I'm not going to say it will damage your hard drive when you move it, because 99% of the time, it won't make a difference, but that 1% chance sucks when it happens. It will take quite a hit to really do any instant damage.
Also, I find the SMS in the Unibodies to be sensitive, but it is only protecting the hard drive better.