My MySQL database does not support UTF-8. Do I have a problem?

No you don't. Versions of MySQL lower than 4.1 do not have built in UTF-8 support. However, Joomla! 1.5 has made provisions for backward compatibility and is able to use UTF-8 on older databases. Let the installer take care of all the settings and there is no need to make any changes to the database (charset, collation, or any other).