Yes, as noted by Arnold Neumaier, all ensembles are equivalent in the thermodynamical limit and the Bose-Einstein distribution applies in all of them. I would just like to anticipate what you are thinking about and point out a few facts

- What most people know about the behaviour of a Bose-Einstein gas applies to an ideal, collisionless gas. Once you introduce collisions, there is no thing such as a one-particle ground state to fall to and the argumentation becomes much more difficult.
- Finite size of the system (finite volume, number of particles) introduces, at least in an ideal gas of free particles, a finite gap above the ground state but smoothens out phase transitions.
- If you want to create black holes by collisions of microscopic (quantum) particles, you probably need $k_B T \approx E_{planck}$. In most thinkable situations, both Bose-Einstein and Fermi-Dirac are indiscernible from the Maxwell distribution at these temperatures.

Anyways, the second part of the question asks about black holes created by collisions. This is hard to comment on, because we do not know how would that actually happen because we have no quantum theory of gravity.

The general thing to remember about gravity is that it has many "antithermodynamic" properties. For instance, increasing the kinetic energy of objects in a gravitating system decreases it's temperature. The question of thermodynamic equilibrium of a general gravitating system is unresolved. Etc. etc. Thus, what you might find is that the black hole creation by collisions might be a runaway process, because every collision with a black hole creates just a larger black hole and larger black holes Hawking-radiate less. I.e., for a certain choice of parameters, there might be no thermodynamic equilibrium, just collapse into a large black hole (which is kinda sorta an equilibrium).

However, you might have some luck with special choices of parameters, the radiation might be strong enough for the black holes to evaporate almost instantaneously (before colliding with more particles) and then the problem is basically the computation of a grandcanonical equilibrium with the chemical potential being set to the energy required for the black hole creation. Any point in space corresponds to the reservoir where the particles can leave at the cost of the black hole creation energy and the evaporation is the spontaneous route back. Of course, this idealization will make sense only if the chemical potential of the black hole creation is *lower *than the chemical potential of the gas without black hole creation. (Otherwise the mean black hole fraction just tends to zero in the thermodynamical limit.)