Not unless you re-subscribe to PlayStation Plus no, however epending on how long ago it was that your PS Plus Subscription lapsed, there is a chance that if you were to re-subscribe your saved data could still be there, I have heard of others letting their Subscriptions lapse but only to see their saved data still intact 2/3 months later afer re-subscibing.
I suppose it may depend how much you want your Max Payne 3 save data back, is it worth $17.99 to find out?
Customer Service Available Mon-Fri 8am - 8pm
General Enquires - 1-800-345-SONY (7669)
Account & Billing Support -1-877-971-SONY (7669)
Live Chat Available Mon-Sat 6am-10pm PST & Sun 6am-8pm - LiveChat