Can I write an if statement within a Javascript object when setting an attribute?

No, however you can use the ternary operator:

var testBoolean = true;

var object = {
  attributeOne: "attributeOne",
  attributeTwo: testBoolean ? "attributeTwo" : "attributeTwoToo"
}

You can use an if statement, if it is within a immediately invoked function.

var x = {
  y: (function(){
       if (true) return 'somevalue';
     }())
};