By my understanding that would need to be supported by the Lemmy protocol directly first to work properly.
The app could just filter out stuff from blocked instances after it gets the data from Lemmy, but then you'd just get mostly-empty pages if you've blocked a lot.
Apparently the Connect app handles it client-side. It obviously doesn't translate over to browsing from desktop or anything, but it makes the app experience that much more enjoyable. Connect breaks my subscriptions though so I can't use it. Would love to see Voyager add this feature though!