That won't suffice for when/if Verizon asks you to verify employment. Of course, you can try.
Don't worry about anything until such time as you are asked to provide proof of discount eligibility. If you already have the discount, let it ride. You can always bring your pay stubs from the state retirement system to a corporate store and have them use it to verification. It will then need to be approved by the finance department. At that point they worst they can say is no and the discount drops off. However, if you currently have the discount then let it be until you're asked for verification.