I think the first level of those swaps would be a (centralized) server operating as the matchmaker, but SAFE doing the notary in the background … e.g. non-custodial, but centralized operations and matchmaking.
The only condition I see is that SAFE has to support hash/timelock transactions (if there is another way to do atomic swaps, I am not sure. But non-custodial servers, even if centralized, are surely most of the way there. And it will work so much faster on SAFE than e.g. BTC (where you may have to wait for confirmations between several of the steps)
With just a few primitives, something like IDEX should be quite feasible on SAFE, but if elders were expected to process lots of logic, it could also weigh down the network quite heavily. As long as an atomic swap process is possible on SAFE, all else will follow.