Not a cohesive impression of the entire play, no. Because it'd take you at least a couple of weeks to read it round the class, glossing a substantial proportion of it as you go, which isn't actually what Shakespeare had in mind for appreciation of his work...
Bear in mind also that not every teenager is a confident & expressive sight reader of iambic pentameter with abundant archaic vocabulary. Not many adults are!
You can understand the play as a cohesive text far better by watching a performance in 'real time'. Although I usually start with a drama improv of the plotline & characters - after 20 minutes, with no prior exposure, my bottom set year 9 could confidently explain exactly what happens in Othello & why.
As for the language, the sort of thing we're looking for these days, is, to give a fairly example, a page long detailed exposition on the symbolism, alliteration, onomatopoeia & foreshadowing contained in the phrase 'so shows a snowy dove trooping with crows'.
Familiarity & understanding aren't at all the same thing, as your 'Wuthering Heights' example demonstrates. Why hadn't they drawn a family tree of characters or a storyboard of the plotline? It's not difficult to teach plot & character, but language analysis is a bit more demanding.
I'm not saying reading whole Shakespeare plays is a bad thing, you understand, given sufficient time. Just that we do have quite a lot to get through in 5 terms to cover two GCSEs, so we have to go in fast, teach some quite high level skills pretty quickly, & move on to applying them to the next text.