First of all, not only can you drive 500 miles, but you can drive it until the car falls apart.
Second. From the look of it that is a cut. Not a crack. It looks like it has been there for a long time. Taking into account the rust that has developed. That sway bar link connection is not going to change.
You can technically disconnect or remove the sway bar links. Your car will drive almost the same as least as far a normal driver can tell. With the exception that you may notice it being less stable when you make sharp turns.
If you want pice of mind have your mechanic weld it where the cut is located. I bet he will not want to do that or recommend it since it won't bring much money.