Whats the worst that can happen when missing your passenger sides sway bar link?
 

I currently here a thump when I abruptly accelerate but it doesn't effect handling or anything... was just curious if this should be addressed soon or not. Thanks in advance

You'll want to repair it as soon as you are able to.

Depending on what car you have there's normally a sway bar to frame bushing as well, one on each side. It's best to change them when you change your links.

The "WORST" that can happen is a dangerous question. The free end of the bar can get cought up in some suspension action, during some extreme conditions. Say hard cornering when the car is leaning quite a bit.

It not very likely, but it can be serious. But it seems to me that it's pretty easy to fix it; just bolt on a new end link.