I would, especially if it is a bad allergy.
Even though you may not order something with strawberries doesn't mean something "accidentally" happens or cross contamination occurs. But with an allergy noted extra precautions should be in place. JMO but that is what I would do.
I would at least just mention it to the server when you get there. They'll probably send a chef out to talk to you. It may not be completely necessary to note it on the ADR, but it couldn't hurt!
My wife works in a resorts' Food & Beverage department and they stress the importance of guests with allergies letting their server know of any food allergies. The server will then let management and kitchen staff know of your food allergies.
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