Oh, so you’re assuming all the air is instantly pushed to the person’s skin? Yeah, that could do it. Actually, if the stuff is pushed arbitrarily close together you get black holes. I read OP as the destination air gets moved out more evenly, and just the vacuum remains.
Supersonic planes do get hot, because the air basically heats until the flow is subsonic again, so they would glow in the infrared a bit. Normal atmospheric pressure, as you noted, isn’t enough to make anything nuclear or even chemical happen.