Bigger hotels tend to have a reservations team. Not every hotel will give you a better offer than whats on booking but depending on how you'll put it on your email etc yes you do get some discount against booking.com. Don't forget that a hotel has to pay 15-20% fee on the booking at booking.com and also has to deal with booking.com's rating system afterwards.
For me so far its worked everytime I am emailing the reservations team at a hotel. (I am in their trade though and tend to use my business email when booking)
I reckon phoning a hotel might be harder to get you a discount because most of the times the frontdesk staff won't put you through to the reservations rep because he might be unavailable or whatever so they'll just give you whatever price the system tells them which is what you'll get on their website if you go to book directly. Its important to be able to contact the person that can amend the booking prices and frontdesk staff usually can't do that.
For me so far its worked everytime I am emailing the reservations team at a hotel. (I am in their trade though and tend to use my business email when booking) I reckon phoning a hotel might be harder to get you a discount because most of the times the frontdesk staff won't put you through to the reservations rep because he might be unavailable or whatever so they'll just give you whatever price the system tells them which is what you'll get on their website if you go to book directly. Its important to be able to contact the person that can amend the booking prices and frontdesk staff usually can't do that.