I've done large sections of the WHW with a trailer, but there's a couple of sections i'd be wary of. the descent into kinlochleven from the Devil's staircase has some pretty big sharp edged drainage ditches, if you can't hop the bike you'll have to slow down a lot for them, and thre trailer wheel might hang up in them anyway. Also the climb, although you'd be pushing lots of that with or without the trailer…
there aren't too many gates or stiles, i managed to keep the trailer hooked on to the bike by dint of picking bike up with one hand and trailer with the other. bit of a strain on the old arms but was worth it for reduced fuss.
the north bank of loch lomondside is a tricky walk with the bike alone, would be purgatory with the trailer. i hear there is a ferry from inversnaid to the west bank, where you can ride along the road to Ardlui to rejoin the way.