Would a Biorock formed buiding be suitable for ocean floor research?
I suspect the answer is no. The reason is that underwater constructions typically are supposed to be air- and water-tight, and to have strength enough to resist pressure differences. Biorock looks like it is naturally porous, so it would not be particularly good at holding water out. While the compression strength is like concrete, you really want to guarantee the solidity if you have humans in it. 

Basically, risk and uncertainty is a cost too. It is often worth paying extra to know what a structure can handle. So hence it might just be easier to use underwater concrete, where there is likely far more standardised quality. 

(Still, biorock is cool and will presumably in due time be well understood enough to compete with a lot of materials and methods.)