What you describe is the process we would use to make the composite today, using bulk manufacturing. That process is far outside our kind of biology. But it is a bit like saying that ants cannot make formic acid because their bodies cannot handle heating anhydrous glycerol and oxalic acid to over 100 C; they of course cheat by using an enzymatic reaction instead.
If we want to show that a product cannot be made by a particular kind of biology we have to show that some necessary step is impossible. For example, depositing diamond is probably impossible with Earth biology because the high energy content in the diamond bonds that have to be made using "tools" made out of weaker proteins working in a water phase. It is less clear that fullerene compounds cannot be made.
We have evidence for life surviving at high pressure (Halomonas saliara apparently requires 1000 atm pressures) and high molarities (halophiles thrive in saturated salt solutions), we have plenty of bioproducts containing very complex crosslinked structures with various kinds of nanoscale order, neutrophil granulocytes actually produce hypochlorous acid (bleach) and there are examples of organisms producing cell-free composites. These are organisms that occur naturally; it seems reasonable that their performance can be pushed much further by specializing them. For example, halobacteria are limited by the energy demands of resisting the osmotic gradient. In nature they can only get energy from sunlight, but in a biotech environment we could supply them with suitable chemical energy directly and at a higher rate (we could even remove large chunks of their metabolism and run that externally). So even if the production of organic beanstalk composite would take something like the process in the paper, it is not that far removed from what conceivably could be done by very tweaked cells.
Chocolate teapots are only useless if they are made of normal chocolate; one can easily imagine a bioengineered "chocolate" that does not rely on fat adhesion for structural strength (maybe some kind of lacquer instead) that would actually work as a teapot. It would of course be unlikely to taste any good.
That said, I think the Pentapods would be stupid if they forgo the tried and tested human materials science (and the existing economies of scale) to solve the problem in a much trickier way using their own technology. After all, using bacteria to nanocrystalise metal is far less efficient than using a forge if you want to make something macroscopic. They would be better off evolving organisms making beanstalk component chemicals like long fullerene strands more cheaply than human bulk processes. Still, if there was an embargo on selling hightech to Provolutionist rogue nations they would be motivated to find their own biotech solution. A bit like Germany using hydrogen in the Hindenburg because of the helium embargo.
