Synchros should never be taken off road.  They will rust up.
And you could lose it.  Its dangerous to have them flying around loose like
that.
In fact, they should never be taken out of the gearbox off road.  Dirt and
grit and funky stuff can get in there.  You'll ruin the darn thing.
Synchros need to stay where they belong, period.
I never, ever took one off road, and I never will.

Horace