What I mean is that it's wrong to link fermentation activity with O2 uptake as the two are not in any way related.
I think I may be confusing things by using the word "fermentation" to refer to two different things: the processes of turning wort into beer (probably what most home brewers mean) vs a metabolic pathway that happens in yeast (what a microbiologist would mean). I'm not a microbiologist, but I should be more careful.
I agree that fermentation defined as a metabolic pathway does not use oxygen to produce ATP. Saccharomyces cerevisiae can use oxygen to produce ATP, but that metabolic pathway (aerobic respiration) does not produce ethanol.
However, saccharomyces cerevisiae is neither an obligate anaerobe (does not grown in the presence of oxygen) nor is it a true facultative anaerobe (can grow either with or without oxygen) as it is unable to synthesize its cellular structures in anaerobios. So yeast does use oxygen during "fermentation," defined as the home-brewer sense, in the growth phase as you say.
Saccharomyces cerevisiae should prefer aerobic respiration when oxygen is present, as that is more energy efficient, but it can use fermentation to produce energy even when oxygen is present due to the Crabtree effect. The use of fermentation to produce ATP when oxygen is present is known as aerobic fermentation (i.e. fermentation
in the presence of oxygen, but without the
use of oxygen). Why some yeasts prefer the fermentation pathway when oxygen is available is not known for sure, although there's speculation that the alcohol produced by fermentation let the yeast out-compete bacteria for the sugars in fruit. How and when Saccharomyces cerevisiae switches between the two pathways seems to be non-trivial and a topic of active research.
To the OPs original point, it's not clear to me what the yeast will do if you add a load sugar from fruit. If they produce any new biomass, they will use oxygen. This is not typically an experiment that people have published results of, as far as I can see. Fermentation is obviously going to increase. Will there be any oxygen use by the yeast at that point in producing more biomass? Will the yeast use the oxygen introduced before that oxygen has chance to negatively affect the beer? Or will the Crabtree effect cause them to ignore the oxygen and just ferment the sugar? These seem like complicated questions which probably don't have a simple answer. Experiment is probably the only way that they can be answered.
However, if you're adding dry hops or cocoa nibs, yeah, keep the oxygen out.