The method you use for making your request doesn't really matter. Whether you call, use online check in, or use TP's fax service, the same thing is happening: your record in Disney's reservation system gets updated with your request. Doesn't matter how it gets there, no one method gets you preferential treatment.
Your odds of getting your requests are determined by a couple of things. First, the request itself. How many rooms exist at that resort that satisfy your criteria? For instance, if you request "upper floor," there might be several hundred rooms at the resort that meet that request. If you request "upper floor, close to transportation and food, odd-numbered corner room facing Epcot," well, you might be down to 5 rooms that will satisfy your criteria.
The other factor is availability. How many guests will be checking out of that group of rooms on the day you arrive? That's heavily influenced by how busy a time of year it is.