No it couldn't. Banner towing is classed as aerial work, just as flying to Spain with your favourite airline is public transport. If Ryanair offered free seats would that make it a private flight? No it wouldn't.
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You'll just have to read it up for yourself.
You should take your own advice FOK. Your example flight is public transport specifically by virtue of Art 260(2)(b), which treats a flight as public transport if
(ii) the flight is operated by the holder of a national air operator’s certificate or an EU-
OPS air operator certificate and any passengers or cargo are carried gratuitously in
the aircraft except for [employees of the operator] or [the operator's own] cargo
(These days, Ryanair's flight is classed as commercial air transport and covered by EU-OPS, not by the operating requirements of the ANO.)
Banner towing is not "classed as" aerial work. Whether or not a flight is aerial work or private depends, by Art 259, on the giving or promise of valuable consideration for the flight or purpose of the flight. The absence of valuable consideration means that the flight is not aerial work.