Yes, in most cases you can pass a special request through with the booking, but please treat it as a request and not a guarantee. When you confirm a hotel booking there is normally a notes or special request box, and what you type there is sent on to the supplier along with the reservation. Requests like a late arrival, twin beds instead of a double, a quiet room, a high floor, rooms next to each other, or a note that the guests are celebrating an anniversary are the kind of thing that travels well this way.
Whether the request actually reaches the front desk depends on the supplier you are booking through. Some suppliers carry your free text straight to the hotel, some only accept a fixed list of request codes and will drop anything else, and a few do not pass notes on at all. Even when the note does arrive, the hotel decides on the day of arrival based on what rooms are free, so it is always safer to tell your customer that you have asked rather than that it is confirmed.
Anything that costs money or that your customer really cannot do without should not go in that box. Extra beds, cots, early check in, late check out, connecting rooms and accessible rooms are often sold as part of a specific room type or as a paid add on, and where the supplier offers that you should book it properly instead of asking in a note. Bed type is sometimes built into the room name too, so choosing the right room is more reliable than requesting it.
Before you rely on this with customers, make a test booking with each supplier you have connected and check what the confirmation shows back, then word your own emails to customers as a request that has been passed to the hotel.