No, PowerNap doesn't work like that.
When you close the lid, macOS directly sleeps, shutting down fans in ~10 seconds if you have them, reaching S3 (Suspend to RAM) state. Radios stay alive a little longer to keep any BT/Wireless connections to speed things up if you're just moving places, then they go dark as well.
If you enabled PowerNap on charging, your laptop will wake up briefly after some time (Every hour or so) after you plug it in, check mails if Apple Mail is open, check for any system updates, and sleep if there's none after fetching the mails (It'll download the updates if there are any, IIRC). If you have setup Time Machine, and the drive is available (locally or via network), PowerNap will wake the system and take a backup every 24 hours, making sure that your backups are always up to date.
Per factory settings, PowerNap on battery is off, so it'll sleep without any disturbance up to a month or so, and will hibernate when the battery is low.
So, yes, the laptop sleeps as soon as you close the lid. But wakes up periodically to make sure that everything is fetched and ready (if it's connected to power, by default).
BTW, There's an actual method called Power Nap involving short naps to recharge. It's not an Apple naming gimmick [0].
[0]: https://en.wikipedia.org/wiki/Power_nap