It sorta depends what you mean by integrity. You will not get martensite from a quench of 316. There is no low temperature transformation that would cause martensite. You can get martensite in some SS's but you have to cool to well below room temp.
On the other hand, since 316 solidifies as ferrite and then transforms to austenite at high temp, if the temp the material was taken to is above the ferrite transformation temp then you may see an increase in ferrite content since the cooling will be accelerated and not allow sufficient time for a more robust transformation to austenite.
This would most likely only be a problem if the ferrite was too high and you were in the sigma phase service range. The moly in 316 will contribute to accelerating and embrittling sigma phase in 316, as opposed to 308.
Also, depending upon the temp involved the moly could segragate to the ferrite portions leaving the austentie portions more vulnerable to reducing sevices.
The practice of quenching is not unusual but I would do it with the supervision of an some authoritative engineer.
Given that its an architectural shop, if thats the application I would say you probably have little to concern yourself with. I doubt it will effect mechanical properties enough to be a problem. However, toughness in that area will be reduced and you will experience a more pronounced ductile to brittle transition if you did CVN testing. But I doubt it would make that much of a difference. Thats why, however, it needs to be done with the supervision of an engineer.