Can I contact a Steam user without befriending them?

You can send them a message via the Steam Protocol:

You will first need to find out that users 64bit ID, which you can do via http://steamrep.com. With this site you can also see if they are trade scammers or not.

Then add the 64bit ID to this URL:

steam://friends/message/id

Then execute it via Win+R or in your browser.

This way you open a chat with them. However, they will get a notification that asks them if they want to answer your request. If they added you anyway, they probably take it.

Steamrep.com even provides a link for that feature in their search.

They have to be online for that though.

A reliable way to contact another user who is not a friend is to get into a small group with them. If he's not part of any small groups that you can join, you can create a group and invite them to the group.

Then you can navigate to the groups under your friends list and start a chat like you would with a friend.