@johnmilk , John, The Nest Cam Outdoor is meant to be plugged into 110 volt plug, so no I would not recommend hooking up to low voltage wire, I believe minimum wire to use would be 14-2 gage wire and 110 v standard outlet. See below the installation manual for camera. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
https://nest.com/support/images/camera-sept-2016/document/Nest-Cam-Outdoor-Install-Guide-en-us.pdf