It'd be foolish of them, I think, because we're a small, weird, and highly demanding audience. But they've done plenty of foolish things before in their apparent quest to own and monetize every imaginable audio waveform.
Spotify has been busy shoehorning their "podcasts" (on-demand audio shows) into every nook and cranny of the app people use to listen to music. If they notice or think of classical music, one can only imagine how they'll try to "highlight" it.
Classical music has a lot of nuances (some of which are listed on the announcement page) and from UI/UX perspective it would be quite difficult to mixed all these details in the standard Apple Music app.
I'm now wondering what Spotify thinks about this matter. Do they plan to highlight classical music like Apple did. I don't know.