Sub.10 minutes is not enough to even get the engine oil anywhere near up to temp. To fully charge a car battery takes quite a while, thus the number of short-hop battery problems, particularly in city/near suburban vehicles. And, partially charged batteries have a very short life.
A fully charged lead-acid battery (12 volt) will read 12.6 volts, disconnected from anything for a half hour. If you can see 12.7 to 12.9 just after charger disconnect that false plate voltage should quickly bleed off to about 12.6.
My STS has a 18 mA parasitic drain - it sits in the garage on a Battery Minder 24/7.
Best bet is the keep the car connected to a 0.8 to 2 Amp Battery Minder overnight. There are types that permanently connect to the + and - battery cables (where - doesn't matter) and the 110V plug hangs out at the grille. Park it, get out, plug in the extension cord.
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........ speaking as a past diesel submarine Main Power Electrician's mate.