Can anyone tell me if coconut would effect someone with a nut allergy?

Coconut allergy is relatively rare
Coconut is a very different plant from peanut or tree nuts. The presence of the letters "nut" does not mean that coco-"nut" will trigger an allergic reaction in people allergic to peanut or tree nuts. The relative frequency of allergy to peanut and tree nuts (relatively common) compared to those allergic to coconut (very rare) would suggest that the risk of coconut allergy in an individual known to be allergic to peanut or tree nuts is very low, so much so that allergy testing to coconut is not considered as "routine". At the present time there are no published studies examining how often people allergic to peanut or tree nuts are also allergic to coconut. The limited knowledge that we have would suggest that the risk is very low. So what to do if you are worried?
Allergy testing to coconut
If you have concerns about the risk of allergic reactions to other foods (like coconut or other foods), ask your allergy specialist about whether skin prick allergy testing or blood allergy testing (eg. ImmunoCap) testing to coconut is available. Commercial extracts of coconut are not currently available for skin prick testing in Australia or New Zealand, and currently no single "coconut allergen" is available either. In this situation, sometimes "crude extracts" of the actual foods can sometimes be used for testing.
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Coconuts are not nuts. They belong to the palm family along with dates, palm cabbage and sago. Allergy to any of these foods could increase your potential to be allergic to coconut.

Generally people who are allergic to nuts do not react to coconuts because of cross reactivity but rather the person's high predisposition to developing allergies. In that case, any food would be just as likely to develop into an allergy.

This being said, processed coconut, can contain sulphites to preserve the coconut and maintain its white color. Individuals can react to the preservative (whether they have a nut allergy or not).

My daughter has an anaphylatic allergy to nuts. Coconuts are not a nut, and she can eat them. However, processed coconut MAY contain a nut warning because it has been made in a facility that processes nuts.