So if the person wanted to enforce it and the document is written well they can.
However the customer really would be the ultimate deciding factor. If its a customer they wish to keep or not keep. Or the type of relationship they have with that customer.
Lets pretend it is comcast. You work for a comcast prime and have a non-compete, and then comcast approaches you or you approach them (which would be grimy.) and asks you to work direct with them. You could advise comcast of your non-compete and see if they can ask the Prime in question to release you from that, in regards to them. Its not likely they say no, if Comcast forces the issue as Comcast controls their work also.
The best thing to do is work outside of market for however length of the non-compete and then work on your own contracts. If you agreed to a certain term you should honor that term, regardless of being sued or not, or at the very least ask to be released from sub obligation for a certain customer.
At the end of the day your word is supposed to be your bond. Dont start out breaking your word not a good place to be.
