Yes, overloaded ports can be very audible, even at high drive levels. But it depends. If the port is rear or bottom-mounted, that can do a lot to mask the chuffing noise. The chuffing can be heard because it is a very distinctive sound. They can be accompanied by other unwanted noises as well. In some cases, when the speaker is sub is pushed to the point of chuffing, the driver will also be complaining from over-excursion. Also, chuffing comes at the expense of the intended sound, so when the speaker/sub starts getting to that point, you can hear it because the clean bass is replaced by fluctuating wind noise from the port.
Tubular ports are almost certainly the most optimal for reducing chuffing since they maximize the volume to surface ratio. In other words, there is as little surface area to create drag as possible. If I were going to design a speaker with port noise elimination as a high priority, I would not go with a slot port.