The Candlelight Processional set up does not block the street. Some vehicles may pick up/drop off in a slightly different location, but I believe they all still run. Below is a picture from Dec 1 2023. You can see the Candlelight Processional set up in the background and the Horse Drawn Street Car running in front.
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The vehicles don't run during parades, cavalcades, and when the
Disneyland Band is marching down Main Street. Some vehicles are used to transport VIPS during special events and during cavalcades. For example, right now, the double decker bus, yellow horseless carriage, and fire engine are used for the Halloween cavalcade.
@Hobbes, no, they do not run in the evening. You can find the timing on the app if you search for "Main Street Vehicles." Today, they are running from 8 am to 3 pm. Of course, tonight there are two evening parades and fireworks which make it impossible to drive a vehicle on Main Street.