Yes but if your press alt-whatever it generates a character that may not be a euro on everybody's computer, whereas if you spell it out € in the HTML code it's guaranteed to display as a euro symbol on any computer (if the computer has a € in any of its fonts)

Same with £ which sometimes displays and sometimes doesn't if you use the £ symbol on your keyboard.
Again spelling it £ (as I did above) always works.

Anahata