If I had an allergy to a food and I take a Zyrtec (cetirizine) daily, will it prevent me from noticing symptoms like hives?

Not likely . Antihistamines like Zyrtec (cetirizine) can help to treat mild symtpoms of an allergic reaction like hives, rash, itching, or sneezing. However, it would not prevent someone from noticing a food reaction. Any severe food allergy should be treated in an emergency room setting. .
I would not. I woul dnot eat foods you are allergic to just because you are taking an antihistamine. You could still ahve a bad reaction.