Yes, it definitely should be a feasible method.
Yeast will rapidly (within a matter of hours) consume the oxygen that has been provided, at which point you may provide it more and it will happily accept. The important point in determining the quality of the subsequent fermentation, as you suggest, should be how much oxygen the yeast consumes in total.
There are a few practicalities, however, that may make doing this accurately somewhat difficult:
How you provide aeration can matter a lot. I used to do this by shaking a full carboy. The initial aeration is not so difficult, but once fermentation gets going (which ideally will be very rapidly) carbon dioxide will almost immediate begin to saturate the wort. This means that, if you go to shake to aerate more several hours later (say somewhere between 2-12), you can potentially have a gushing mess on your hands. Even if you are using an air pump with a stone, this may cause violent foaming.
Unless you have a dissolved oxygen meter, you won't have any way of knowing how much oxygen remains unused by the yeast when you add more. So you won't have any good way of determining how much oxygen in total has been added. In general, this should be fine since over-oxygenation isn't a huge concern in home-brewing and it's typically better for us to ere on the side of caution (more oxygen, rather than less). It will just become a matter of trial-and-error to see what works best for your particular fermentation techniques.
Experiments have suggested that the optimum time to oxygenate your wort is actually a number of hours after yeast pitching. These experiments also suggest that when added at the optimal time, the amount of oxygen needed may be as little as half that needed when adding right at yeast pitching (i.e. if you used 16 ppm at pitching you may only need 8 ppm added at 4 hours to achieve an identical fermentation). This is most likely due to the yeast membranes becoming increasingly functional as they move out of the 'hibernation' (or stationary) phase into active fermentation, and so becoming better able to utilize any given amount of oxygen as time progresses (up to a point). So you may see how this effect could lead to difficulty accurately matching the amount of oxygen added to the amount needed by the yeast when adding over a period of time.
'[H]ow long should one aerate in order to get the benefits of higher DO levels?'
I would actually suggest doing oxygen addition in 'batches', or discrete additions, several hours apart, rather than as one continuous addition. If you have a method you're fairly confident is saturating your wort (i.e. to ~8 ppm oxygen) start with that, then repeat that maybe 4 hours later. I would play around quite a bit too (try it at 2, 4, 6 hours &c; try it for half or a quarter of the initial time; stuff like that). Every yeast strain has its own particular needs for oxygen, and will react differently to receiving more oxygen some time after the initial dose (in any given wort, no less) so saying just how much you need to oxygenate and when is basically impossible.