My own experience is that you can go a scant number of miles that way, but not a lot. The problem that comes when you get a shoe blowout of that sort is that, Murphy's law being in effect, you're probably 50 miles away from your next planned trail exit.

Duct tape, at least the one time I tried it, lasted significantly less than a day before becoming inadvertent trail litter. Just in general, I find duct tape to be useless for dealing with footwear issues (gaiter repair might be an exception, haven't encountered the need personally).