To answer your question, yes. You can edit the contents of an object and that will reflect in the original object, but if you try to overwrite an entire object (the reference of it), you can't.
You can view an example in this jsfiddle (select Run top left):
https://jsfiddle.net/kcx61hye/34/
var player = {number:1};
var player2 = {number:2};
function Renderer(player) {
this.player = player;
this.player.number = 4;
}
function Renderer2(player) {
this.player=player2;
}
document.write(player.number); //Outputs 1
Renderer(player);
document.write(player.number); //Outputs 4, so object is modified
Renderer(player2);
document.write(player.number); //outputs 4, so no modification