Photopass+ cards are only good for 14 days from the day of activation. They do punch the card on the lanyard with the date it's good until. So, you can't activate one on your first trip and use it on the second, as it will expire before then.
In January, I took two trips within a two-week period. I didn't activate my Photopass+ until my second trip, but had no problem adding photos from my first trip once the account had been activated. Mind you, these were just regular Photopass photos--no ride photos or character meals--just standard "in front of the castle" pictures. I kept the cards from those photos and added them to my Photopass+ account the day I activated it on my second trip, two weeks later. Worked like a charm and no problems.
So, in theory, I think it would work, at least sort of. You wouldn't be able to get any ride photos or character meal prints from your first trip--just regular Photopass photos. You'd keep the cards. Then, you'd activate the Photopass+ on your SECOND trip, add the cards from the first trip, and you'd be good to go. As long as the second trip is within 30 days from your first trip (while the photos are still stored in the system), it should work. Since your trips appear to be almost exactly a month apart, you will probably have to pay the $15 to get the extra time on the first sets of photos, though, so you'd have time to edit them after your second trip.
You would have to decide, of course, whether not getting ride photos or character meal prints from the first trip is worth the savings.