Yes. A CDMA phone that is roaming ("extended network" as Verizon calls it) will use more power and drain the battery faster.
This is because in addition to doing its normal phone-like things on the extended network, the phone is also periodically scanning for signs of a decent signal on the home (native Verizon) network. If it can find even a weak Verizon signal, it will even try to handshake with that network a few times before giving up and staying on the extended network, until it feels its time once again to scan for a home network.
This is something baked-in to the baseband profile. Every call on the Extended Network costs Verizon extra money, because at the heart of it, you're roaming, just like old-school cellular users did back in the 80s. Verizon just isn't charging you for it outright.
Clearly, the sooner they can get your phone back on a home network tower the better (and cheaper) for them, so they program their phones to check often for home signal when roaming. Which costs energy. Which reduces battery life. And if that means they can blame the extended network for you having to charge your iPhone more often, well, so much the better for them... from their point of view, it's another disincentive to get you to avoid roaming if you can.
I'm not sure what Verizon sets for a polling interval, but it's probably on the order of every few minutes or so.