Confirmed in Browserstack. The ?s= gets immediately appended to the URL on load, and the modal is opened.
Leaving my notes here for @jsnmoon hands baton
I tracked it down to the onInput handler for the input in SearchBox. You can add some debug to the setSearchQuery action to see it happen.
In most browsers, we see a single setSearchQuery to null when the page loads:

In IE11, the onInput is unexpectedly fired when the page loads, which leads to setSearchQuery being called with the value "" (which now opens the search modal).

(The forEach error does not seem related but bears further investigation - related to querySelectorAll calls I suspect.)
I've discerned the cause: IE11 immediately fires an onChange event if the input placeholder contains a Unicode character. Guess what our placeholder for the search input includes?
… <- This.
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I've discerned the cause: IE11 immediately fires an onChange event if the input placeholder contains a Unicode character. Guess what our placeholder for the search input includes?
…<- This.