Yes, it would, if only small branches are involved. Otherwise that would be overkill. The best time to do it is in the morning when all the caterpillars are still in the tent.
Dispose of pruned off material as above under Black Spot. After a few weeks you may add the material to your compost. For bigger branches or for tents in the crotch where two branches meet, or if you don't want to prune, a more "hands-on" approach is necessary.
Armed with a pair of gloves, a brush, sponge and a pail of warm, soapy water , simply wipe the whole nest into the pail and scrub the area clean. Rinse with clean water. Be a good neighbour.
If your garden borders public land and you notice tent caterpillars there, you may as well destroy them too or they will re-infest your garden. More.
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