I don't think it matters if you are booking yourself or through a TA--if the rate is not available with Disney then you won't be able to get it no matter what. I think you have a better chance of getting one with a Disney Specialist TA because he/she is generally on the phone with Disney for a good portion of any day, so the more times on the phone the more chances to keep looking for the room to become available. The TA does the leg work for you to try to get you the best rate possible.
Room requests are not guaranteed with Disney, so again, whether you book the room with a TA or Disney directly a request is just that--a request. Disney tries to honor requests but cannot always do so.
Sue Ellen