I noticed that in the description it makes absolutely no mention of Xbox Live awareness. Just to make be sure, does this mean that the game won't even alert me if I've gotten a message/invite?

No, you are not able to use the dashboard or guide button while playing and Xbox original. It's like being disconnected from Live while you are playing.

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You'd be suprised at how many Halo fans don't know that the Master Chief is a slave.