Yes, you can check it on GST portal. There is link for it.
Click on Search Taxpayer link in GST portal. You can search every registered person there.
It is really a pain to ask each customer and collect these details. Think of a situation, suppose when you asked to the customer whether he is under composition or regular scheme and he answered composition scheme.
But after 10 days he migrated to normal scheme. Will you ask each customer again after every month.
It is a real concern.