not in my experience with so called biochar which its actually just charcoal.
Humic acid, humate, leonardite which is a complex carbon source does proven increase microbial activity in the soil favoring fungal dominance and also reduces ammonia loss from urea and there is evidence to prove it. Its about bioactive functional groups like polyphenols and not just dead carbon.
This is a pretty complex question. First of all, biochar is diverse in its properties, such as compost, vermicompost, and even soil, depending on organic input, temperature, duration, and much more.
To answer your first part: Biochar is generated in a pretty hot process and is sterile. So biochar does not add any microorganisms (MO) to the soil or potting mix, etc. unless the biochar is charged or inoculated with MO e.g. from vermicompost, compost, EM or other. But if inoculated, it should be declared as inoculated biochar or similar.
Does the biochar stimulate MO growth in the soil or growing medium? This will depend on various criteria again. In principle, biochar can increase surface area for the growth of microorganisms if nutrients are available and moisture conditions are right. This raises the question, is the biochar decomposing? Very likely, and therefore, it is not a permanent carbon sink in the soil but a carbon source for decomposition. (I know this is a challenging statement for some scientists.)
The Nitrogen cycle in a soil or growing medium is complex. Even if biochar absorbs nitrogen as urea, ammonia or nitrate, it is a question of for how long and how much before saturated. In the end, the nitrogen is released, and from here, it depends on the uptake (plant or MO), gaseous release from the soil, or leaching below the root zone.
There is no simple answer, and we should be careful to generalise findings from one trial ...