We just did this recently, bumping up from Southern California Select to Deluxe & Signature, and adding Maxpass (we didn't have it on the passes before). Our renewal date is in mid-September.
As soon as I agreed to the upgraded renewal and made the first payment, our passes were upgraded effective immediately, including the Maxpass. I was surprised by it, so I posted on here and ended up calling the Annual Passport line. The CM I talked to said that it's not "supposed" to go into effect until the renewal date, but sometimes "the system" upgrades you early, and she checked my pass and said it was upgraded. We went to the park last week and confirmed that our passes were indeed upgraded, with Maxpass functional and everything.
So, long story short: An upgrade on renewal is not supposed to take effect until your renewal date, but it might. Your mileage may vary!