Possibly: just dont waite to long to do it. as it Could show on your credit report.! Call Customer service an see if you Qualify for a New line or Lines if so go for it .
Verizon will do a credit check when you open the account, and depending on the results, they will ask you to pay a deposit. You'll have the chance to review the deposit amount and accept or reject it before your order is finalized.
I think most people are able to open postpaid accounts with bad credit, as long as they pay the deposit. If they outright refuse to let you open an account, you could look into prepaid service until your credit begins to improve.