Yes, in most cases you can send a special request along with the booking, but it is a request only and never a guarantee. Our hotel booking API accepts a free text remarks field on the booking, so you can type things like late arrival, high floor, quiet room, honeymoon couple, or adjoining rooms if possible. That note travels with the reservation to the supplier and on to the hotel, and it also shows on the voucher your customer carries.
What happens next is entirely up to the property. Most hotels read these notes and try to help, but they only confirm on the day based on what is actually free at the time. Some suppliers also pass remarks on exactly as written, while others shorten them or only accept certain standard codes, so a long paragraph may not arrive in full. For that reason it is best to keep the note short, clear and in simple English, and to put only one or two important things in it rather than a long wish list.
There is one request worth treating differently, which is a late arrival. If your customer is reaching the hotel very late at night, say so in the remarks and also check the hotel policy text on the room you are booking, because some properties release rooms if the guest has not arrived by a certain hour unless the booking is guaranteed. Requests that cost extra, such as an extra bed, airport transfer or early check in, usually cannot be handled as a free text note and need to be either booked as a paid item where the supplier offers it or settled by your customer directly at the property.
When you book, set your customer's expectations by telling them the request has been sent but is subject to availability on arrival, and suggest they mention it again at the front desk at check in.