Switching off the OIS might be relevant for higher shutters maybe. I.e. over 1/1000. I'm not sure if it can cause problems when the shutter is fast enough, I'm guessing here so I might be completely wrong.
The other question is how well OIS works in combination with the 1.4x converter. Obviously it works well with lens alone, but perhaps there are issues with OIS using the converter that create problems.
As mentioned, I'm not saying these emphatically, I'm just surmising what potential issues there could be.
Maybe, but I've never seen evidence of OIS introducing issues with the TC attached in any of the countless images I've taken with that combo. To be honest, I've also never bothered to switch OIS off regardless of the FL I'm shooting with that lens... with or without the TC attached. Not saying that there might not be something to that issue, but it's never bitten me -- and the 100-400 is arguably my most used lens.
So, I'm not going to recommend one path or the other here. Only stating my own experience which suggests that leaving OIS on
may have little or no impact regardless of shutter speed. At least that's been my experience and I'd encourage folks to do their own evaluation and share their results.