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Not really, the words are pronounced differently

Although I've seen the email address burger@[domain] and wondered why anyone would have an address named after a food - until realising the sender was a Mr. Burger (pronounced like this: https://upload.wikimedia.org/wikipedia/commons/f/fe/De-Burg.ogg + er).

Also, the food burger is pronounced almost like the Americans do because we took the English pronunciation and modified it slightly to fit existing German sounds.

The "ü" in Bürger however is pronounced like the "ue" in the French word rue, which is a sound that doesn't exist in English.