If Russian gov. succeeds in shutting down the WT and the other churches that compete with ROC, the move will have an extremely powerful negative impact on Russia and eventually on ROC; the rest of the modern world is looking and may correspondigly act upon Russia accordingly.
Are they shutting down "other churches" as well? I thought it was just Scientology and Watchtower.
Most of the "rest of the modern world" knows very little about JW's. They just see JW's as annoying wierdos who knock on doors at inconvenient times. Those who care about principles of religious freedom tend to be from the liberal left, which doesn't have as much influence at the moment, especially since the recent USA election.
With a new gov. pending in America that favors trade with Russia...
The new Govt may favor better relations, not trade. (Russia has nothing to sell but oil and military equipment.) Another reason that there may be little fallout.
if WT wins in that Court if it has to go that far ( and WT can't loose )...
Long story short: It is very hard to predict what the European Court of Human Rights might do.
Overall, I don't think anyone in the West will be that interested. I doubt the issue will get much media coverage.