Many people are skeptical about the effects a tired battery can have, but especially in older cars you can get all sorts of odd behaviour. One of the issues can be that the various control units (ECUs) are programmed to "expect" certain characteristics of voltage, for example voltage recovery after cranking and start, and if it doesn't fit within the expectations then the ECU can adopt "non-standard" behaviour.
One classic was with old VW Golf models (I'm talking very old, early injected models) where the afterstart fuelling would go haywire with a tired battery so you'd get start/stall issues.
If a battery is more than a few years old it is well worth considering replacement anyway, not expensive by today's standards usually (compared to fuel for example).