This seems very unlikely compared to the obvious answer that they added a crappy antenna to keep their BoM and assembly costs low.

The radios on these are weak and adding an Omni antenna is exceptionally unlikely to violate EIRP.

Could this design accidentally radiate something it's picking up from the board outside of 2.4ghz? Sure.

But practically it's quite unlikely to in this context.

2.4GHz is already incredibly crowded and prone to interference (in urban environments). I remember once picking up emissions on a Bluetooth headset from a leaky microwave oven.