Certainly, but that's different topic than the same-day or overnight shipping that you were asking about, no?
Currently those fulfillment centers only use trucks. (I spot checked a few Amazon fulfillment areal photographs on Google Maps.) They would have to be relocated on rail lines, or lines moved to them. There would need to be about 4x more centers, since trucks are about 2x faster. Probably more like 6x more, since trucks and roads go places that trains can't get to because of grade limitations.
Only you know what 'realistic' means to you. We know it's possible to have a rail system that reaches most towns in the US - that's what we had until the automobile. Many of the right-of-ways still exist, but they were also designed for slower, lighter trains than we have now. And for days with more canned and pickled goods that weren't so time sensitive.
Trains don't scale down. Consider a small town grocery store. Currently it will get several different trucks making deliveries - soda, beer, fruit and veg, etc. These make deliveries to many different stores in the area. How does it work if we switch to delivery by rail? Does the train drop off a trailer bundled with all of the daily deliveries? If so, how are thing kept cool that need to be cool? Or are multiple trailers dropped off, and if so, where are they stored and how much room is needed? Does the store need to be next to the tracks?