Definitely not.
Here's a video of a science reporter, Veritasium, staying in an anaechoic chamber for one hour, in the dark. Not only they do so at the first attempt, but they come out of it convinced they could have stayed indefinitely -- that there was no "driving crazy effect".
Clearly this is weak evidence by scientific standards, but the evidence those links give is no better, and this is actually on film/tape. Also, claiming that something extraordinary happens should be backed by stronger evidence than... nothing happens.
More importantly, there have been studies on whether anaechoic chambers and darkness give hallucinations or psychotic states. This is the subject of this other answer, which finds that there is an increase in the incidence of such occurrences.
That said, the subjects in at least one experiment were subjected to three hours of isolation in an anaechoic chamber. I think this debunks the claim thoroughly.
Imagery Sequence in Sensory Deprivation, R. Vosburg, et al., AMA Arch Gen Psychiatry. 1960;2(3):356-357. doi:10.1001/archpsyc.1960.03590090112016.
