Yes, if the battery is not recharging the engine will not run properly.

While driving our 1991 300CE several of the dash warning lights came on simultaneously and the engine started to run poorly. A short time later the engine simply died. Jumping the battery would permit the car to be driven a few miles until the engine died. Turned out the voltage regulator brushes were worn down to nubs preventing the battery from recharging adequately.

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Fred Hoelzle