Today, when we click the dedicated button to copy a HEX value, either in the Color panel or in Swatches Options dialog, Illustrator selects the value (and copies it), but the fact it gets copied is nowhere stated.
I’d use the Ai’s 'shy message' to inform the users about this instead ( '#XXYYZZ copied') and would not select the value — but would select it by clicking the '#' symbol instead, to match the 'click the caption to select the value' paradigm Illustrator uses in all other fields.