Possible. The battery light comes on when you turn the electrics on. So if it's making contact slightly between the two ignition positions (off and electrics on). Plus on the MK2s, the ignition barrel is a common failure point. You can usually tell, if you can scan it for codes it'll throw up things like this:
00849 - S-contact at Ignition/Starter Switch (D)
008 - Implausible Signal
00466 - Control Module for Steering Column Electronics (J527)
004 - No Signal/Communication - Intermittent
00883 - Ignition Switch (D) Terminal S
012 - Electrical Fault in Circuit