Well, for now, and given my fairly limited experience (I've done 7 trips in the range) I'd say go for it. The forecast for Mirror Lake says 40% chance and that the rain is supposed to come as scattered thunderstorms. I looked at it hour by hour and it looks like the evening will be pretty clear. Bring your rain gear and expect to get rained on a bit, and I think you'll have fun. For added security, you could go somewhere with a shorter hike in (Clyde Lake or something), so that way you can have your tent set up early and have a place to go in case of rain. And if the weather really sucks, you can just pack up and leave since the hike out is short.
I'm weird in that I like being out in adverse conditions sometimes, but I'd check the forecast from a few more sources, and then make a decision based on that.