Can AnkiWeb shared decks be used in AlgoApp?

Yes; many decks are available directly within AlgoApp; simply perform a search for the deck from the "Get Decks" screen.

If the deck(s) did not show up in the results, you can manually import the shared deck(s) you have downloaded (APKG files) in app using the Import Decks option.

See: Can I use my existing Anki (APKG) decks with AlgoApp? for more details.