If you’re lucky enough to have a cooperative display, the RetroTINK does indeed allow for instant switching between 240p and 480i when outputting in a linedouble mode.
Unfortunately, you’re not gonna get instant resyncing when the RetroTINK is connected through the OSSC, regardless of whether it’s set to passthrough or linedouble mode. I tried it myself.
If you’re in North America, TCL’s TVs from 2017 (the P607 and S405 series ) are fantastic for use with the OSSC and RetroTINK. They can handle 5x modes from OSSC even with the troublesome SNES and NES. They can also allow for seamless 480i / 240p transitions when directly connected to a RetroTINK. Input lag is around 14ms, which is just under 1 frame.
Here’s a short video I took of multiple 240p / 480i transitions on a SNES going via a RetroTINK to my TCL 55P607
SNES 240p – 480i Transitions