It is not a good idea to use any phone with a Lithium Ion battery while they are plugged in for extended periods of time. This can cause a lot of stress on the battery and possibly wear down life. Of course its fine to use it for short periods of time like quick browsing, texting, and emails but i wouldnt recommend gaming.
Totally inaccurate. If that were true, you should not ever use a laptop while it is plugged in either.