Most anacruses are less than a bar long. Often a one note pick up. An example that brings up my question is 'Fur Elise', which seems to have a pick up which lasts for four beats (in 3 time), before the tune proper starts. Is it a fact that an anacrucis can last, well, as long as a composer wants?
When your editor suggests calling it a "prelude", you might be overdoing it. As a rule of thumb, it has to fit in a pickup truck.
Joking aside, the only hard limit is what your editor is willing to accept. Usually the mark of an anacrusis is that it fits with the beat: for a 3/4 beat, that puts the plausible limit at something like 2/2 when starting with a partial hemiola. If you start with an actual unmetered cadenza or something which might more reasonably be called a meter change, limits become fuzzy.
But all those are common-sense limits, not hard music theoretic ones.
The situation here is that time signature and the bar lines don't correspond to the "beat" of the music. We don't know why Beethoven notated the piece in 3/4 time, but rhythmically there is one beat per bar not three, and the first bar line corresponds to a weak beat not a strong one. So you are correct that, with Beethoven's notation, the anacrusis is four quarter-notes long.
Beginner pianists might not prefer the piece to be written in 6/4 time using half the number of bar lines, or in 6/8 time using 16th notes, but those notations would make the "problem" disappear.
Beethoven habitually used this type of notation in faster pieces. The scherzo of the ninth symphony has the instruction "Ritmo di tre battute" (i.e. three bars of 3/4 are really one bar of 9/4) and later "Ritmo di quattro battute" (i.e. four bars are really one bar of 12/4). See http://imslp.org/wiki/Special:ImagefromIndex/108612 pages 9 to 12.
I'm not sure what kind of official answer you're looking for. Four minutes, 33 seconds?
In Rhapsody in Blue, there's a trill and a glissando, both of which can be stretched as long as the clarinetist wants.