Yes. External house lighting, especially in higher-than-average-crime Arizona, is probably going to keep the numbers up. Also headlights from cars, though there shouldn't be much of that past midnight.
Ever walk around in a bad area at night with few lights?
My experience. Was waking in what I thought was a decent area. As soon as sun dropped sketchy looking character were everywhere. Just standing around doing nothing. I assume selling drugs. When I got back to an area with better lighting they were all gone.
* You don't want your house to be the juiciest target. Having lights prevent it from standing out as a place where someone could just hide in the shadows.
* Lights make your cameras more effective.
I'm not really living in a bad area (town homes go for around $1 million here), but we are close enough to a large unhoused and/or drug-seeking population that we still get a lot of property crime (mainly smash and grab on street-parked cars, but you see people going around looking into houses as well). So while everyone on my street is fairly wealthy (and can be relied on to let you know if something is wrong), we still have to do our due diligence (lights, motion lighting, cameras).
Lots of anecdata here but no actual data. If it’s just something that moves crime around, then it’s just people lowering their personal risk to let others pay the externalities. Or maybe external lights reduce the absolute amount of crime. I don’t know.
What kind of data do you want? It isn't like this can be funneled through a controlled experiment, but non-personal security (military, corporate, etc...) has always relied on extensive outdoor lighting to deter theft. My guess is that it is always just a game of whack a mole (the amount of crime stays the same, it just gravitates to less protected houses or less protected neighborhoods).