Is there any way to set up WebSphere logs to go to the
console (as in http://myeclipseide.com/enterpriseworkbench/help/index.jsp?topic=/com.genuitec.myeclipse.doc/html/quickstarts/websphere6/index.html)
but also to a file?

MyEclipse will redirect what it can to the console, but as far as how to further configure WebSphere, you'd have to check the docs.

Let me ask a follow-up then. You recommend putting 'console' into the
File name field of the JVM Logs configuration, which allows the
redirection to MyEclipse's console. How does that work, then? Is
'console' a special file as far as WAS is concerned?

I believe console is a keyword that WS uses to know to redirect to stdout and stderr which is what MyEclipse redirects to the console.