Sending extra letter of recommendation before submit app

<p>My research mentor sent an extra letter of rec to colleges in mid-October, but I submitted my actual apps in late December. If the colleges received the supplemental letters before they got my application, would the letters be lost, or would they be waiting there for my app to come in? The schools were Harvard, Yale, Stanford, Princeton, and Columbia, if you know anything specifically about their policies.
Thanks!</p>