If you run off your car battery it do of course put a extra load on the battery, but its not like it will slash your car battery's lifetime from 5-6 years to 1 - 2 years.
No matter what option you go with, you still have to drive enough for the battery to get charged in relation to how much you use the battery when you are parked.
So if you only drive a hour every day and expect to use the camera in parking mode all the other hours of the day you will be in trouble i assume.
I myself are for the first time about to be able to try parking mode in a camera of mine, but i will only be using timed parking guard for 30 minutes or so after i park, that will cover all of my shopping time in car parks, and at home i dont need it as i have a CCTV camera on my car where it is parked. ( apartment car parked in back yard parking lot, CCTV camera on balcony door )
And if i should one day use a little more time as i will be parked out on the town, then i can just enter the camera and select a longer time frame for the camera to be in parking mode.
If you have a larger vehicle, like a truck, then you might be able to have a second battery installed, and have it isolated from your main car battery like the camper / RV people have.
This way you have a whole battery just for the camera alone, and isolated it can not discharge your main battery.
This setup are sort of like the new dedicated dashcam batteries also work.
This is a route i would go myself if i had a larger vehicle, but sadly this side of a lotto win i will have to live with my shoe box sized little hatchback and its one little battery.