can I run the test suite without a web server?

You’re on a Mac! You have two of the three components you need for a Web server by default. Apache and PHP. All you need to do now is get MySQL. There are plenty of tutorials on how to do this and can be found with Google.

Of course NW Tech recommendation of MAMP is another great option. Especially if you haven’t managed a server before. Check out the WordPress Codex.