I use EPAuto for my 2018 Honda Fit EX multiple times with out any issue. I plug it in into the cigarette power.. I turn the engine on. I think that was recommended to do. I did had the first honda battery change to some other brand now. But yea, shouldn't be a problem using it with the engine on.
PS: I lost count how many times I use it. Haha. I normally remove some air and put in air every 2 to 3 weeks. There was one time one of the tire stem was leaking air I had to add more air in. But yea, it is a great tire pump.
As for the honda battery I think I have it more than 2 years and the voltage drop was around 11.4 volts. Normally should be 12.1v to 12.4v.
I recommend getting this attachment. Easy to lock into the stem and very easy to remove.. This is what I got: https://www.amazon.com/dp/B07MXBYPT2/ref=cm_sw_r_cp_apa_glt_fabc_B7V7SBRCWX9SJ0TGWWHD
If you don't use that I notice when you unscrew it from the stem you loose like 1 to 2 PSI.