There are no specific rules preventing studying whilst claiming benefit because of incapacity for work.
I wouldn't see starting a course as a relevant change of circumstances unless the reason you can now attend is a significant improvement in your health (and then the improvement would be the relevant change.)
The DWP probalbly consider it should be notified as the sort of tasks that they do while attending the course may suggest that they no longer satisfy the Personal Capbility Assessment.
The PCA should not be effected if they are - exempt - have a disability that clearly means they score enough points to satisfy the PCA, e.g. a wheelchair who cannot walk at all.
There is also no reason why someone should not be entitled to DLA while studying. In fact it may be easier to show they require frequent attention and so a higher rate may be payable, e.g., a person awarded only low rate care but needs a sign interpreter to attend college.
A bit of a ramble but I hope it helps.
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