No, it usually means the opposite. Esters, particularly polar di-esters, are great at cleaning. The reason you see high oxidation with esters is because ester contains oxygen via C-O and C=O bonds, a result of carryover of the alkyl group from the creation process. (reacting acids with alcohols)
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The FTIR machine, which measures oxidation, cannot discern harmless oxygen in ester from actual oxidation (where hydrocarbon bonds are broken and replaced with oxygen) thus it all gets read as oxidation.
This is one of the cases where UOAs can be misleading for someone who doesn't have background knowledge of oil chemistry, formulating, lab equipment, and analysis processes. Much like many things in our world, data is only as accurate as the knowledge of the observer. Hence, anecdotal claims are wrong >80% of the time. It's also why UOA comments are wrong, or at least missing the mark, about half the time since the rookie techs in these labs aren't often fully educated in lubricant chemistry. Thus, they flag stuff that things that shouldn't be flagged. This is why BITOG exists to help eliminate these confusions.
Some things to note though... not all esters have the same oxygen content. It can vary wildly depending on the type and feedstock. Thus, you may have 2 oils with the same ester concentration (say 10%) with one showing oxidation of 20 and the other showing 60 because the 2 oils are employing different esters. So note that just because one oil has higher virgin oxidation than another doesn't mean it has more ester or has a linear increase in ester. VOAs are important for knowing things like this so you know where your start point is. You can calculate your actual oxidation increase relative to the virgin oxidation value. Relative oxidation is usually condemned when it reaches +25 over virgin value.
EDIT: Also note that the oxidation value from ester does not indicate how well that particular ester cleans. Just because one ester shows higher oxidation, at the same concentration, doesn't mean it cleans better. The two parameters are unrelated. A high virgin oxidation value merely means ester is present in some substantial amount. It doesn't tell you how much, which type, or how well it cleans.