If my customer does not turn up at the hotel at all, will I still be charged for the room?

Yes, in most cases you will still be charged, because a guest who does not arrive is treated by the hotel as a booking that was never cancelled rather than as a booking that was called off.

What exactly happens depends on the rate your customer booked. On a non refundable rate the whole stay is normally charged and nothing comes back. On a rate that allowed free cancellation, the hotel is still usually within its rights to apply a no show charge, because the cancellation deadline went by and nobody told them the guest was not coming. Many hotels also release the rest of the stay once the first night is missed, so a customer who simply arrives late may find the remaining nights have been given away.

Through the hotel API you can cancel the booking or raise the no show with the supplier, but whether any money comes back is the hotel's decision and not something your portal can settle by itself. The booking will normally change to a no show in your admin area once the supplier passes that back, which can take a little while after the check in date. Your own position with the customer does not change on its own either, so if you have already collected the money it stays with you until you decide what to return.

The practical thing is to tell your staff to cancel in the portal the moment a customer says they are not travelling, even if it is past the free cancellation date, because a proper cancellation is almost always treated better than silence. Check the cancellation terms shown at the time of booking so you know in advance what a late change will cost you.