The more splashing, bubbling, surface agitation you can get the better the aeration is going to be. However, if there is not much to bring the bottom water to the surface, you might still not get enough aeration especially during hot weather when the water doesn't hold as much oxygen anyway.
If the water trickling back into the fish tank is going to be enough will greatly depend on the size of the fish tank, the fish mass in the tank, amount of additional biological oxygen demand in the tank, and the temperatures you are dealing with as well as the total flow rate and design of the system. For instance, if you are simply flowing water from a raft bed into the fish tank from the height of 3 or 4 inches at a rate of say 2 gallons per minute and you don't have any additional aeration in the raft tank and you have a large fish load, I would say NO the water trickling back to the fish tank won't be enough. Or if you are doing timed pumping and there are long periods of time between water flow when there is no water trickling back to the fish tank well then probably NO it's not enough.
As to the bacteria, they colonize all wet surfaces in a system. However, they do best on wet surfaces that are dark and get plenty of access to well oxygenated water. Flood and drain gravel beds are great for providing those conditions though constant flow/flood beds work well for it too as long as the flow is enough to keep the water throughout the bed well aerated.
Initially the bacteria need to colonize the system and we call this cycling up a system and this process usually takes 6 weeks give or take depending on conditions. Look up the nitrogen cycle and cycling up a system or fishless cycling to learn more about the process.
Once the system is cycled up, the bacteria have to have access to the ammonia and then the nitrite before they can convert it so it isn't really instantaneous. Generally a properly sized system though the fish produce the ammonia at a rate that the bacteria can convert before it reaches a measurable range to us normally and same with the nitrite. Most of the time we shouldn't be seeing spikes unless there is a sudden change in feeding, fish load, temperatures or other disruption. Now if you were to cycle up a system and then "dose" enough ammonia to say bring the system to some set ppm of ammonia all at once, then it is going to take some period of time for the bacteria to handle that amount of ammonia, they don't do it instantly, they can't it takes some time for the ammonia to disperse into the water even. However the test to say a system is "fishlessly cycled up" is when you can dose to 1 ppm of ammonia and within 24 hours have both the ammonia and nitrite levels reach 0.
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if you use the search function both if these topics have been discussed at length, particularly the oxygen one