Yes, underlined text intuitively invites a visitor to click on it. More importantly, do not underline text that is not a link.

Sometimes, the placement of text that are links such as headings in the top-right corner of a page are obviously links for navigation. They may not need the underline in their idle state, but they should change with a mouse-over with color and/or an underline.

I have never been a fan of the "visited" link state. I tend to leave a link, visited or not, looking like a fresh link.

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DrTandem's San Diego Web Page Design, drtandem.com