Battery Life
I found out that I can still connect to my monitor when my power cord and the HDMI cable is connected to my Mac while it's closed. However, will my Mac overcharge and ruin the battery life?
MacBook Pro 13″, macOS 10.13
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Your battery should not overcharge.
If your curious about the health of your battery, here is an excellent link from Apple on battery health management in Mac notebooks (Intel only).
This link provides information on optimizing battery and diagnosing problems.