Yes, in most cases your customer can add a special request when they book a hotel on your portal, but whether the hotel actually does it is never guaranteed. The request is passed along with the booking, it is not something the hotel has agreed to in advance.
How the request reaches the hotel depends on the supplier behind the rate. Some hotel connections accept a plain text note that travels with the reservation, so your customer can type something like a late arrival after midnight, a quiet room, or a room away from the lift. Others offer a fixed set of choices instead, such as non smoking, twin beds or a double bed, or honeymoon stay, and anything outside that list cannot be sent. A few older connections pass nothing at all beyond the guest name and the room type. Because of that, you may see a request box on some hotels and not on others in the same search, and that is the supplier, not a fault in your portal.
It also helps to set expectations with your customers in writing. A bed type, a floor, adjoining rooms or an early check in are requests, not confirmed parts of the rate, and the hotel can charge for some of them on arrival or simply say no if it is full. Anything your customer genuinely cannot travel without, such as step free access or a cot, is safer handled by contacting the hotel directly once the booking is confirmed, with the reference number to hand.
Run one test booking on your own portal and look at what the request field offers on a few different hotels, then add a short line to your confirmation wording telling customers that requests are subject to availability at check in.