Short answer: Likely.
Maybe techniques from powder metallurgy can be used to sift carefully selected grain sizes together for high density bricks. Depending on the microscopic shape of the mineral particles, it might be possible to have them fit together nicely. (I imagine that mineral particles that were formed in space might have remarkably different microstructures than those on earth.) Dry dust in a vacuum could be carefully sieved and deposited into a vibrating mold in layers to get close packing. Particle sizes could be selected so that successively smaller particles fill the voids left by larger ones.
With little or no atmosphere, it's trivially easy to get perfectly dry powder, which is important for the sintering. If there is any offgassing during the bake, the final material is likely to be porous and open-celled. In fact, the near-complete lack of gas in a lunar environment would mean there would be no gas entrained in the microstructure, at all, when it comes time to bake. It's perfect!
With dense, water- and gas-free powder, and long baking times one might be able to get sinterred bricks that are almost non-porous, or at least closed-cell so that they can be air-tight. A thin coat of sealant might be needed on the interior surface in case of wormholes.
I don't know about mortar though. It might have to be a polymer mortar because most other types of mortar will offgas as they set, so they will definitely be porous and open-celled.
This type of structure might be preferable to the plastic bubble construction we often see in science fiction. With non-porous brick and polymer mortar you get a sturdy, insulating structure that is not prone to accidental damage. As a bonus, because the polymer is between the bricks or inside the structure, it will not be exposed to UV radiation, so it will not degrade by that UV denaturation.
A structure like this doesn't have to be a tomb either. It can have glass windows, provided the windows are well sealed and are thick enough. (They don't have to be very thick, either. Imagine windows that can keep water out of a submarine at 3 meters depth.) Sure, glass is fragile, but it's a lot tougher than a sheet of polyethylene and it will last much longer. Again, glass is something that can be made on site with a solar oven, provided there is silica dust to be found. Silica is pretty common throughout the solar system. Organic compounds might be hard to come by in a space colony so it's best to minimize the need for them.