They wouldn't be able to learn our language just from watching us speak. In order to learn any language, a conversation has to take place. You have to say something or hold up an object and have them respond to it. If you hold up a ball and they say the same thing every time you hold it up, you can safely assume that what they said was ball in their language.
/Geek Rant
Uh. . .well. . .
We have computers than can break coded messages by using numerical algorithms. Some colleges are trying to apply them to ancient languages.
If aliens reached Earth they must have attained a technological level that enables faster than light travel. You'd figure they'd also have computers capable of deciphering our speech through context cues, pattern-recognition, and similar algorithms.
/uber-geek-counter-rant

EDIT:
Actually nobody knows for sure what it sounded like. Modern Church Latin is quite different from later Roman Latin, which was again very different from the Latin spoken in the late Republic. There is no such thing as a 'proper' Latin pronunciation, the best you'll be able to get is an educated guess made by linguists.
I was taught that Latin was still a spoken language when early French developed. Some early Frenchmen wrote transliterations of Latin into French. Scholars 'know' how early Medieval French sounded, so they were able to piece Latin pronunciations together.
Additionally, since it formed the basis of all Romance language, once would guess it sounded closer to Spanish/French/Italian than Germanic/English.