Do acetic acid bacteria use the electron transport chain when converting ethanol to acetic acid?
Yes

I find it somewhat ironic that in a response a recent post from the poster concerning itself with the precise definition of ‘fermentation’ I argued that this was a semantic question because of the use of the term in the English language before any biochemistry was known. I now discover that the term is used in an even looser sense than I was aware of — in an aerobic context. The conversion of ethanol to acetic acid by acetic acid bacteria is apparently referred to as oxidative fermentation as explained in this extract from a paper in The Journal of Bacteriology: 


  Acetic acid bacteria are obligate aerobes that belong to the α-Proteobacteria and have a strong ability to oxidize ethanol, sugar alcohols, and sugars into their corresponding organic acids. Such oxidation reactions are traditionally called oxidative fermentation, since they involve incomplete oxidation of these compounds. These bacteria accumulate the corresponding incomplete oxidation products in large quantities in their surrounding environment.


The biochemistry is summarized by Gómez-Manzo et al.:


  Ethanol fermentation by acetic acid bacteria is carried out by two sequential reactions catalyzed by pyrroloquinolinequinone (PQQ)-dependent alcohol dehydrogenase enzymes (ADH) and aldehyde dehydrogenase (ALDH), which are located in the cytoplasmic membrane [6] and transfer electrons to ubiquinone Q10 [7]. PQQ-ADH is a periplasmic quinohemoprotein-cytochrome c complex and catalyzes the first step of ethanol oxidation by transferring electrons to Q10 and producing acetaldehyde which usually is the substrate for another enzyme (ALDH), and converted to acetic acid during the second step of ethanol fermentation.


The fact that the reduced pyrroloquinolinequinone is re-oxidised by ubiquinone, indicates that the conversion of ethanol to acetic acid requires the electron transport chain in the bacterial membrane to continue, and that the ultimate electron acceptor is oxygen.