From my experience, it probably should. I ran into trouble recently trying to salvage the bottom of a cider yeast cake, however that turned out fine after I pitched a packet of Lavin EC-1118 into the must. The EC ate all the dead yeast and fermentation has been textbook since then.
The only thing I would recommend is that you do a soft pour into the yeast cake and add yeast nutrient. I'm not an expert by any standard, but I think that trying to manually oxygenate after pouring a few galls of apple juice/cider would leave ou at a severe contamination risk. Also, I guess you should re-cork your carboy that has the yeast cake after racking to the bottling bucket or keg.
With juice/must (especially store bought/cheap juice) you have to keep in mind that you are making the 21st century equivalent to the accidental alcohol that helped teach the human ancestry 10,000 years ago. If you use one of the cheaper juice sources these forums recommend you have little to lose from a spoiled experimental batch. Think like Randy Mosher; let the yeast sort it out. Radical Brew till your heart is content.