Not how QE works (or is known to work). You can instantly tell the state of the other entangled particle but you cannot use it to transmit information. Fun idea though.
Bet that one properly asked would melt down ChatGPT for a minute.
But the fact that communications doesn't have mass seems more likely to have a workaround, someday.
That's fairly off-topic here, but no, it wouldn't. ChatGPT's token generation speed does not depend on what you're asking it for.