Yes, they can tell you whether or not you get the preferred rate or the standard rate. I did this with my son in January when we were in WDW and we just bought in June. The preferred rate in June was 10.75% (same as in January).
I do not believe that this has anything to do with down payment. I believe 10% down by close is standard. At point of sale (when you say, "Lets do it send me the papers.") you put down $500 minimum and when you return the papers you provide the remaining down payment and provide account info for monthly draft.
Also I would suggest multiple contracts in 50 or 100 point increments. For exampe:
150 points = three 50 point contracts
200 points = two 100 point contracts or four 50 point contracts
There are threads on this board that discuss this, but only Disney can do this at original point of sale. If you need/want to sell later small contracts typically have a higher resale value per point than larger contracts and usually sell faster (so I have heard). Also if you do need to sell, you would not have to sell all of your points, but could do it incrementally. It is also handy if you plan to leave them to your kids, at some point as you can designate specific contract to a particular child. There may be others but those two are what mattered to me as we did three 50 point contracts at SSR and Disney paid all closing costs.
Good luck