Yes if you make it stoop and remove all the baggage.
The gates of Jerusalem are called the eye of the needle and camels are just to big to get through so the only way to do so is above in the day time but at night it must go through the smaller gate which meant it would have to crawl on its hands and knees unencumbered.
Alternatively the story goes that the saying derives from the Greek word kamilos but when translated into Latin it became kamelos meaning camel. So thus can you get a camel through the eye of a needle and it depends on which translation to whether you can.
If a horse and carriage would fit, I'm sure a camel would.
I also thought about somebody flying a Sopwith Camel through "The Needles" - a rock formation on the South Coast, but couldn't find whether they have any part called an eye.