First of all it is not correct to refer to a thermostat as an “ensemble”. I have been explaining this many times on this mailing list, please see in the archives why this is incorrect.
From what it seems based on your descriptions, you are likely not in any kind of the usual, well defined statistical mechanical ensembles (they usually require having a homogeneous bulk system and no other manipulations like fix momentum or fix setforce or fix wall/… or others). Whether you have a well defined statistical mechanical ensemble or not is independent from whether you have a meaningful simulation or not, or whether applying a thermostat and what kind and how and where is required or important or not.
Yes, what I was describing is an important test, but it may also be required for the “production” simulation of your system.
Again, it is not possible to provide a definite answer to such a question without knowing more details about what exactly the system and input is and what kind of system you want to represent and compare to. Either using a thermostat or not using a thermostat may be more adequate.
You need a thermostat when you simulate only a subset that is embedded into a buik system. For adsorption studies, especially with particles deposited from gas phase, you may want to apply the thermostat only to part of the system, i.e. the part that is in contact with the bulk (usually that part requires some kind of boundary to immobilize the system in space which represents being coupled to a 0K system which needs to be compensated for), but then time integrate the surface and the deposited particles without a thermostat applied (because they have either an explicit thermal coupling or no coupling at all).
This is much more a question about the science of your simulation than about LAMMPS, so my advice is to discuss this with people sufficiently familiar with your research and also with statistical mechanics to discuss the implications of different choices. There are no simple “do this, not that” kind of general rules in these cases.