Urea is known to form hydrogen bonds with water. Will it react with the carboxylic acid side chains of proteins in aqueous solution to form a covalent bond? or will it form both, covalent bond with carboxylic acid and hydrogen bond with water?

A hydrogen bond is very different from a covalent bond. When you dump urea in water, there is no covalent bond between the water and the urea, just an electrostatic attraction.

 

To the best of my knowledge. urea doesn't really do anything with proteins under normal circumstances. A urea derivative is actually a side product of a peptide formation process used in the lab, so it really wouldn't make much sense to have it damage the product.

 

On the acid side of things, urea really isn't very acidic or basic (although it does break down into the basic ammonia), so it shouldn't really do much to carboxylic acids.