In short: no; HTML 3 only, before CSS.
The "HTML" supported by JLabel, JButton, etc, is things like and to provide inline styling of label textual content.
To indicate that an HTML supporting component contains HTML, the string value must be wrapped in ""; this is for backward compatibility with existing code. For example:
button = new JButton("Two
lines");
JLabel does not provide an implementation of the CSS 2.x visual formatting model, so HTML4 style="" attributes and CSS box formatting will not work. If you want rich HTML formatting support then you'll need to use a web-browser component.