If I sand this bump down will the drywall start to fall?
Drywall is not held to ceilings or walls via mud/tape.   The mud/tape is used to hide seams.   So sanding should not effect how it is fastened to a wall/ceiling.
In your particular pictures you have a seam that almost surely has tape at the top right in the picture and then a stress crack down to the left.   The stress crack may or may not have tape.
I can bet on two things from the picture above...

I don't think there was a repair in this section.   Well there could have been but not at the border of the entire crack.   It would be very hard and silly to cut out drywall at weird angles.   To me this is original job then a crack patched up.

If you do sand it down and do whatever to it after, more than likely whatever you do will end up looking like this.  There is a buckling of this drywall going on and sanding it and retopping it may work for 2 months, maybe 6 months but go through a full seasonal cycle and you will be back to this eventually.


What can you do?

you need to clean out the cracks that have been patched.   I would take a chisel and scrape out everything that is raised.  If you can get the full mud strip that would be ideal, until you are a good 2-3&quot; past the &quot;issue&quot;.
I would then create a &quot;v&quot; notch along the seam with a full 1/4&quot; gap at the bottom of the &quot;v&quot;.
Fill the gap with caulk.  This is messy and may require 2 layers.
Reinforce the drywall with more screws.
Resume with normal mud/tape schedule.   If this is an extremely sensitive area it may be better to use spackle or some other wall topping that has more elastic properties.   (There are also additives available for joint compound)
If it is a REALLY sensitive area you may also want to use an elastomeric paint.   This is a bit extreme and I am not sure if they even make these for indoors (but I have used outdoor elastomeric paint for stairs areas in homes that kept cracking).