It’s going to depend on existing (or even new!) merchant processor services adding Ark support in their systems, rather than the Second team building it directly. We’ll definitely be working on getting integrators in the merchant space, but it’s probably going to come some time after launch on mainnet (that’s our priority right now!).
Unless I’m missing something, I think it’s unlikely Ark will help much with the EUR conversion side of things. Whether a merchant is using Lightning, on-chain, or Ark to receive bitcoin, conversions are always going to need some kind of third party to swap with.