In short, yes. But the longer answer is that ‘it depends’.
There are 2 main materials used for making most mini whiteboards;
PVC and MDF with a hard coating.
MDF with a coating is nearly impossible to recycle so these unfortunately have to head to landfill.
PVC is also very tricky to recycle.
Show-me boards however are made from neither PVC or MDF but PP which is super easy to recycle, just pop in your normal recycling bin.