No, all fonts do not support all crazy characters. I work for a printer and while we can get our fonts to work on screen, some printers do not support things like the euro (€), different arrows, M dash, N dash, some degree signs, fancy double quotes, actual inch marks (as opposed to a double quote), etc.
One of the problems is we must have at least 20 different Helvetica font varieties, not included bold, italic, and bold italic. Thus some of the Helveticas might support the euro, some might now, and Helvetica is a super common font.