Yes, it comes down to how the DPCM channel encodes sound data. A sawtooth gets most it's energy and harmonics from the sudden jump at one end. This impulse is impossible to encode in 1-bit delta encoding, the closest you can get is a slightly steeper slope. The audible effect is similar to a low pass, with the strength dependent on the intended amplitude, so instead of a nice sharp saw, you get a muddy not quite triangle.

A few commercial games did use the DPCM channel melodically, but the main drawback is the large size of the samples relative to the commonly available ROM chips of the era. Price is a big factor when you need to put one chip in every game. Here's how that sounded in practice:

https://www.youtube.com/watch?v=LEgoYUzwabI