Unless you insist on rest days, it would not require 100+ mile days, at least not most days. Actually, 3,058/36 is just under 85 miles per day average. That would mean long days, but it definitely is not out of the question. The question would be more "do you want to push that hard", rather than "is it possible".
Remember that the time of year folks ride the ST typically has short daylight hours though, so you are likely to need to start early every day and ride through most/all of the available daylight and maybe into the dark at times.
Depending on my motivation, fitness level, and the terrain, I find an average of anywhere from 50-80 mile per day to be pleasant, but I am a not so athletic 60 year old, so if you are younger, motivated, and/or more fit/athletic you might enjoy it.