I would run it. As far as 4th gear Synchro issues I would say forth gears usually nothing that I'd bang unless I'm racing or something more so use third to get the speed and nice easy shift into 4th?
I rebuilt mine couple years ago (for the first time) and put the $99 rebuild kit in it, new synchros, steel shift forks (had brass), new 1-2 and 3-4 shift leavers coming out of side cover and two new ears to connect to them on the outside. That's a connection that quite often gets overlooked and if you want to tighten that up no time like the present.