A trivial answer : yes. When I was quite young I wrote a computer program to spit out a succession of 'beeps' at random frequencies not related to any musical scale; I suspect many people who have a computer and a bit of an interest in music have done the same. In practice how close you could get to infinity (!) would be limited by the resolution at which the computer could represent pitch, but conceptually that's a case of continuously changing frequencies.
The thing is, once you have decided that you have all frequencies available to you, what do you do with them? If you've listened to compilations like the Computer Music Journal sound anthology, Computer Music Currents, or Cultures Electroniques, you'll probably have heard pieces made up of non-scalar pitch grains or gradients (sorry, I can't remember the titles of any examples!). Some of these are fun, but to someone with fairly conventional musical tastes they can sound like variations on the sound of someone's broken plumbing; many listeners tend to yearn for harmony, which means forming relationships between pitches, which brings us back towards scales again.
There's another sense in which “∞-TET” is perhaps closer to commonly-heard music that we might think, in that a lot of styles use glides/bends/portamento in a way that is integral to the sound of the music, but does not necessarily tend to be notated precisely. Blues is the most obvious example, although it tends to be more free in some ranges of the octave than others. I'm also thinking of some Eastern vocal styles, and quite a lot of violin playing (even in the classical tradition).
Musicians will also stray from ET tuning towards more pure 'Just' intonation where possible, so this is another sense in which music isn't really anchored to a fixed set of pitches.
In a way, perhaps you are describing a type of atonality that isn't limiting itself to a 12-tone scale; on the other hand, The concept of atonality is usually associated with avoidance of an obvious tonal centre, which wouldn't have to be the case just because the music is freely-pitched.