Hi,
Are you referring to the PCV hose? If so, yes that will cause a vacuum leak, but I would think the vehicle would have a rough idle or stalling issue.
Do me a favor, repair or replace the damaged part and see if the smell goes away. An engine vacuum leak will cause the computer to compensate by adding fuel to the air/fuel mixture. Take notice if there is any dark gray or black smoke from the exhaust. If you do, follow this link to check both the fuel pressure and the fuel pressure regulator.
Let me know what you find. Also, if you could take a pic of the hose you are referring to, it will help me identify it.
One last thought. If you have a strong fuel smell in the oil, change the oil. If enough fuel is mixed in, it will cause the oil to thin.
Take care,
Joe
See pic below.
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Thursday, October 13th, 2022 AT 9:05 PM