I have a 3 fixtures each with 4 fluorescent tubes with ballast replaced about 8 years ago and these fixtures are connected to the same switch in the kitchen. This am there was an smokey smell and the fire department believes it originated from a bad ballast. I removed all tubes from the offending fixture of 4 and I am wondering if current will still flow through the 'bad' ballast if I turn on the lights to the other 2 banks (again on same switch).
Yes, it could.
Here is a somewhat typical ballast. As you can see, if one of the many components has failed short, current will flow from active to neutral. The diodes in the rectifier part of the circuit or one of the transistors can fail in this way.
If they are oldskool inductive ballasts, then removing the tube will open the circuit.
If they are electronic ballasts, they're like power supplies, so even without tubes installed they will be powered.
However if there was smoke or "fried electronics" smell it is possible that some wires have melted insulation so I'd really recommend opening up the fixtures to check. Cut the power from the panel, you never know if the light switch really does cut the live... or if Protection Earth is actually connected... Better safe than sorry.
Remove the ballast cover from the fixture, if the ballast is not already exposed. This cover attaches with screws or inserts into slots cut into the fixture. Replace the ballast if it appears burned, swollen or is leaking oil.
IMPORTANT: Flickering fluorescent tubes can cause the ballast to overheat and fail prematurely! They can even cause a starter to burn out! Don't wait too long to fix the problem or you may end up with a bigger repair!
Which type do you have? Tube p/n?
Modern "instant start" passive Ballasts short both end pair pins in tubes and source and do not use a heater in tube.
"Instant Start" use high voltage strike with no heaters and are in parallel.
All Yellow are common.
They also have shunt ballasts so each other tube still works if any one fails or is removed.
Usually the failure is not so much the ballast but the tubes after 5 years when they get contaminated and draw excess current. If the ballast is not protected and left too long , it begins to overheat.
Modern tri-phos tubes should last 10 yrs or 50kh.
Smells like the series old tar type to me and not the new ones. No worries for now. No problem with tubes removed.
Replace all ballasts and tubes with new parallel type, lower power more efficient 86 LPW similar to many older LED types. I prefer tri-phosphor true white only. 4500'K