No, but elbow failures are most likely.

Spokes fail due to fatigue, with the number of cycles (about 750 per mile) dependent on both mean stress and the magnitude of the variation.

When the elbow is formed not all of the spoke is taken past its elastic limit thus leaving areas with high residual stress far beyond everyplace else in the spoke so non-stress-relieved wheels at sufficient tension always fail first at the elbows.

With insufficient tension you might get spokes going slack and bending near the nipples for a high variation and failures there.

Personally I gave up on wheels built by machines or shops with potentially marginal mechanics about 15 years ago and haven't had a broken spoke since then. Jobst Brandt (author of _The Bicycle Wheel_) claims over 100,000 miles on 15/16 gauge double butted spokes which are properly tensioned and stress relieved.