IMO don't mix work and play, if you value your job!

However, for sure it's a good opportunity to try game-y type things and experiment (obviously keeping within sensible professional boundaries), eg. watching their body language, looking for IOIs, developing observational skills, seeing how they react to your different body language, voice tone, eye contact, question wording, qualifying them, etc. There's a lot you could try and learn while still keeping it professional.