It's true humans have been shown to survive amazing windchill extremes. Just look at the guys who made the first successful ascent of Denali in the winter. The bivied for several days in a tiny snow cave during temperatures of -50 to -60 with wind speeds of 100 mph, wrapped in little more than half-frozen down sleeping bags and 60s mountaineering gear (their bivy sack, an old parachute, blew away.) They all survived with moderate frostbite on their fingers and toes, but they survived. Art wrote a great book called Minus 148. Definitely worth a read or seven.

That's the thing.  They were able to build a snow cave.  If you get caught in a bad storm in Anarctica and you can't build a shelter you may not survive in a tent.  But even though the weather is extreme in Anarctica it is I believe predictable.

Ya,  I guess after seeing the Shackleton documentary and reading about the other treks I have had the worst images in my mind.  After reading up on the topic I find a few things.  First there is a 460 mile route from the edge of the Ross Ice Shelf which makes it a lot more doable compared to a 2000+ mile trek.  Also,  in summer the temperatures usually stay above -45 with lighter winds.  During the hottest days of summer it can stay around -15 at the pole.  But the worst weather is not actually right at the pole.  

So this sounds doable as it makes a journey no more than 30 days.  Since you don't want to get caught in fall or spring weather.  Which you may not survive in a tent.  Assuming you could cover 30 miles a day by bike 75% of the time by going at a slow pace in a very low gear it would make for a 15 day or so trip.  But you would need to plan on enough supplies to survive for 30 days on foot if necessary.  The most challenging thing would be the danger of the crevasses on a bike which you could easily ride over by mistake.  And the wind blown snow dunes are almost impassable with a bike.  You'd have to carry your bike for certain distances.  You could put the bike on the sled for certain sections.  

Since you have to carry a months worth of food the load is heavy and you need high calories so eating butter and bacon type stuff is in order.  The question to ask is if it can be efficient enough to succeed with a bike.  Or if you can built a bike that can hold up for a month and continue to function.

The biggest problem in dealing with a south pole assault would be a way to deal with the temperatures.  You can get -70 degrees F with 70-80 mph winds which will kill you if you don't have an insulated shelter that can be staked down.  This is something like a -200 F windchill temperature.  A tent will be inadequate. Two giant expedition down parkas and sleeping bags will be inadequate.  A team of individuals that can together built an ice shelter would be helpful. 

Perhaps it would be possible to build a lightweight sled with an enclosed area for sleeping and hauling extra gear and food.    Four inch thick foam walls and six inch thick floor covered with a thin aluminum cover to protect it, and a thicker aluminum sliding surface. If the bike breaks, you can continue on foot pulling the sled.   Even rubber tires will fail in these extreme conditions.