The colour of blue dwarf stars
I emailed the authors of the paper, asking whether blue dwarf stars could


  "become hot enough to pass the thresholds for Type B or Type O"


and one of them replied:


  "We use the term 'blue' to mean 'bluer', so that when stars become
  blue, they get hotter than their usual main sequence temperatures. ...
  The point of the paper is that smaller stars get bluer ... But 'blue'
  does not correspond to a particular temperature, and does not mean 'as
  hot as an O star'."


So it looks like I read the H-R diagram correctly. For the stellar masses represented therein, none of the blue dwarf stars actually reach a high enough surface temperature for type B or O, and white type A stars are the closest any of them will come.

However, that doesn't answer the question for stars with stellar masses not represented in the diagram, for example $0.15M_☉$, $0.13M_☉$ or $0.135M_☉$. The authors of the paper didn't run their simulation for these, and there doesn't seem to be enough information in the diagram to make deductions regarding their suface temperature. So until more research is done in this area, the question of whether any blue dwarf stars can actually become blue remains unanswered.