I think it's always a matter for debate whether modern day compositions can generally compare to classical ones (not referring to the particular comparison to Puccini) - especially in terms of quality. But if any modern day composition can be compared, I think some of Freddie's work would be one of them.
A number of reasons. Let's get the obvious part out of the way first, though: they picked classical - pop/rock combinations based on looks and then rationalized after the fact. It wasn't a serious, scholarly piece or anything, so that's perfectly alright, as Puccini did look vaguely similar to mustache-era Freddie.
In my opinion, there are a few crucial musical differences between Freddie and Puccini that make Puccini one of the least likely operatic composers to compare to Freddie.
First of all, musical philosophy. Freddie was notably casual in this respect - he did not belong to a 'school' of composition, he readily moved from genre to genre, he referred to his music as "disposable pop" and, especially in the '80s, he often lost interest in a piece midway, leading to rushed songs (The Works, Mr. Bad Guy). Puccini, on the other hand, was very self-consciously part of a school of composition: verismo, an Italian-operatic pendant to literary naturalism. He embraced some modernist tendencies, like limited chromaticism, but he consciously remained true to romanticism and never strayed from that. Puccini was a musical perfectionist (especially with regards to orchestration) who would never allow a piece to be performed until he was 100% satisfied it was perfect. Also, perhaps most importantly of all, Puccini put form ahead of melody and harmony as the most important musical aspect of any composition, whereas his melodies, though very pleasing, are often extremely simple by operatic standards. Freddie was a melodically-oriented composer, as one can tell from Bohemian Rhapsody and March Of The Black Queen: the sections are shaped by the melodies, not the other way around. The conscious development of a motif throughout a number of sections would seem very alien to Freddie.
Second, lyrics. Freddie was a very capable lyricist, but also a very cavalier one: he did not hold his lyrics to insanely high standards, sometimes coming up with breathtaking poetry, at other times just blurting out a few seemingly random lines, and apparently valueing both alike. Puccini was almost neurotic in his insistence on lyrical perfection. Possibly brought on by the failure of one of his early operas, Edgar, partly because of a poor libretto, he was unusually involved in the writing of librettos for his operas, insisting on revision after revision and not infrequently rejecting finished librettos when, upon contemplation, he considered them not quite good enough. He got into tremendous fights with librettists, and his publisher frequently had to mediate before actual violence broke out.
Third, intent. Both Freddie and Puccini were crowd-pleasers, no doubt about it. They relished the appreciation of the audience and thrived on it. But whereas Freddie never sought recognition of his music as 'high art', Puccini throughout his life felt deeply grieved that, despite his popular success, he was not considered a Great Composer by contemporary critics (as his work became ever more outdated because styles evolved but Puccini largely didn't). Despite being utterly uninterested in politics, Puccini actively sought an honorary senatorship (the highest reward for cultural achievement Italy had at the time) and was bitter over not getting one as Verdi had. The resulting difference is striking: Freddie's musical style evolved with the tastes of the '70s and '80s, whereas Puccini became ever more divorced from 'modern' music, despite easily holding on to his popularity.
That is not to say that there aren't interesting similarites: in personality - the chain-smoking, the playboy lifestyle (and philandering) - and in musical style - a love of exotic sounds, dramaticism through intense orchestration and a love of the 'pure' sound of vocals, without hyper-affected technique (like overblown vibrato).