You'll get an error, because the API for creating Web Workers simply does not exist in IE.
e.g.
var worker = new Worker('my_task.js');
Will throw an error because Worker is undefined.
If you want to do feature detection, you can check first before creating the worker:
if(window.Worker !== undefined){
var worker = new Worker('my_task.js');
}
Of course, whatever task you've delegated to the webworker won't happen on non-supported browsers, which means you'll need to run the logic on the primary (non worker) context.
Since you post message to (and listen for events/messages from) WebWorkers, if you follow the same approach to your worker task you can just run it in your primary context, and make calls to it in the same way as you would if it were a webworker. This will require some additional legwork on your end, but this way you can easily switch to WebWorkers when you detect it is supported in browser.