I'll have to ponder that a bit and see if I can poke any holes in it.
I may have one... the first time through Reese wouldn't have been in love with Sarah Connor already from all those years of looking at her photo... so how does he end up knocking her up? I guess you could argue she was just that bangable... But if he didn't need a photo the first time through, why would John Connor risk altering history by making him an obsessed stalker the second time through?
Hell, how does he recognize her at all without the photo? I forget if that was a plot point... him knowing what she looked like. The Terminators sure didn't.
These are easily explained. The first time thru Reese could have had an entirely different photo of Sarah or maybe, like Ed says, she gets her picture taken in Mexico anyway. There's really no reason JC wouldn't have a picture of his mom.
As for Reese having sex with Sarah, why wouldn't he bang her? The women of his time have no showers and he's constantly on the run from killer robots, so an 80's Linda Hamilton and a bed ought to be pretty enticing for his character. Once the timeline alters with Reese being the dad, JC knows his dad is Kyle Reese from the future, so of course he knows he has to send him back and decides to save that picture to help him.
What I hadn't thought about before was that we see a different character playing JC in T2 vs. Terminator Salvation. That's really jsut a casting issue, but it could also be used to support an original JC vs. a revised JC with Reese DNA. I also notice looking back on the original that the war is set in 2029, but that preview I saw today said something about 2018. Maybe the war just lasts that long, but seems like another potential indication that we are dealing with different timelines.