Can I send on the wallet card when someone has it, and WhatsApp when they don't?

Yes — that's the 'Wallet first' option on Marketing → Channels, per promotion. Each customer gets exactly one message: the free card lane when they hold a card at send time, WhatsApp otherwise. It never doubles up, it's the cheapest choice that still reaches everyone, and its one honest trade is stated on the page: a card deleted without Google telling us can swallow a message, so pick 'both' if certainty matters more than volume. Campaigns choose channels per send in the composer instead.