You can specify the sampling rate of the Teensy with a bit of fiddling, and the limits depend on what you're asking the audio library to do. The stock Chord Organ's set up to run at 44.1k, using a couple of submixes in the library to do things like set waveform levels independently.
You can also set an oscillator to drive the output pin directly, with just one waveform.
I've got a couple of 'em running at 2,822,400hz instead of 44,100hz. That's 2,822k for one oscillator (I can get four running at 768k), by telling the Teensy its sample rate is something hilariously high, just to run some square and 12-bit triangle and sawtooth waves.
I avoid aliasing pretty well :) and it's definitely a fully digital DAC output. It's just good at being free from aliasing because I'm not concerned about what the sampling rate 'means' in terms of 'usable notes'. The only thing I care about is getting my waves nicer. The Teensy also has a rectangular wave, which is PWM adjustable. That, at 2,822k or even 768k, is quite nice even when it's a really thin pulse…
And of course you could use the square to drive an integrator :)