I agree with fineally, if you can get away with it, lightly sand it to give it a key then paint it.
I have done it both ways, I started to strip the newel post which I did and then some spindles, it was awful, messy, and I even used an enviromentally friendly stripper so it didn't stink like Nitromorse but in the end a builder friend saw it and told me to just sand it and paint it.
I have done the sand and paint at 2 houses, from very dark stained/varnished wood, just sanded to remove the varnish coat, and then over an orange pine one.
You will have to use an oil based paint though as the water based satin paints won't stand up to the knocks (that was from a professional decorator)
Even if you strip the spindles after removing them you will have the newel posts and the handrail, and make sure you don't damage the wood with the metal scraper.