Most anti-biotics or pesticides are highly water soluble. Many are also surface active. Water soluble compounds will be effectively removed via water changes. Also, if surface active, they are amenable to skimming. Furthermore and most importantly, antibiotics are reactive molecules. Their half-lives, especially in a very bright light, are generally pretty short. Based on the name, I would classify Ethoxoquin as an antibiotic...not a pesticide. Antibiotics are expecially reactive and short lived.
What this means is that as long as such molecules are added in minute quantities that they will GENERALLY degrade quickly and/or be exported. Things that degrade quickly will not cycle up.
Things that are water soluble but do not degrade quickly can cycle up, but will be limited to levels dependent on the size and frequency of water changes and their skimmer efficiency.
Of course it is better not to add such if possible. For accidental or incidental addition in small quantities, this is not something to worry about for most cases.
Collin