Infection spread in a building is a valid concern. The distributed crosswind solution will still be very effective and is highly recommend that it be installed. This solution is optimized for employees who wear surgical masks, therefore, the particles this solution is designed to mitigate against are in the E-1 and E-2 particle size ranges, with the majority being smaller than 5 µm. The key tenet to keep in mind is the main objective of this solution, namely, the immediate removal of concentrated aerosol clouds between the worker and the resident [view here in Part 3] during the moment of interaction. It is this function that provides the strongest first line of defense in infection mitigation. Since most E-1 and E-2 infectious particles stay suspended in the air, yes, an HVAC system would collect them from an infected room and distribute them throughout your building especially if your HVAC system does not have HEPA filters.
In a more complete answer to your question, infectious aerosol spread would happen regardless whether or not you have crosswind units installed throughout your building. As such, there would be no difference between an installed distributed crosswind solution and no solution, but only on the first air exchange by your HVAC. If you install a distributed crosswind solution building-wide, on subsequent building volume exchanges, every room that contains a crosswind unit would contribute to the reduction infectious aerosols. A distributed crosswind solution would begin to behave as a large high-MERV filter helping your central HVAC, and therefore be of benefit to all rooms.
That means all other rooms would participate in removing the infected particles from the initial cloud emitted inside one room, rather than subjecting every resident to continued suspension and buildup of infectious aerosols throughout your building. Furthermore, because crosswind units keep air in motion within each room and are placed in the vicinity of every resident, there is no chance of aerosols aggregating into hazardous stagnant clouds.
In short, your HVAC system would help to disperse the initial infectious cloud into its building volume diluting far more than in one room alone without HVAC, and then, your distributed crosswind units would provide the subsequent removal.
Surprisingly, this hand-in-hand solution would provide faster and lower the risk of infection even further in a building equipped with HVAC than distributed crosswind units installed in a building with baseboard heaters, where a potentially infected worker generally may typically visit several rooms over his shift.