I'd say you could chance a walk up, but if you're staying at any Disney property, the front desk Concierge can make any ADRs you want for your entire trip. Any Guest Relations in the parks or Downtown Disney can do it, too.
I'm taking the "I'm staying at the Poly for part of our trip" to mean that you'll be either at another resort or offsite. As long as you can get to a front desk Concierge or a Guest Relations location ahead of time, it should be fairly easy to get an ADR just in case.
Normally, the first week of February would be a really slow time of year, but you never know if the new promotion for Jan - June of 2009 will attract more people....especially the Jan - Mar trip dates with $200 bonus gift card.
I think you could probably take your chances as a walk up, but I favor the "better safe than sorry" plan.