After Nintendo starts charging for subscriptions for online play, there will no longer be any free online play, at least using Nintendo's official servers. Doesn't matter whether you're using SX OS or not.
If someone develops something like Wiimmfi for the Switch, free online play may be possible. But that's a ton of work, and probably many years away.
However, X-Link Kai could possibly simulate a local wireless connection, bypassing the need to "emulate" Nintendo's servers. This sounds far more plausible and has been used to avoid needing to pay for other online services, like Xbox Live, in the past. I wouldn't be surprised at all if people started using X-Link Kai for Switch online after the subscription plans go in effect.