The fact that the Switch sits vertically in the dock would make that a pretty precarious proposition. You'd have very little keeping it from just falling straight out the front. Of course, if you leaned the dock back somehow, you'd be golden. Honestly, that's probably how the dock should have been designed in the first place; pretty much the same as a Wii U Gamepad charging cradle:
Hopefully there'll be a relatively inexpensive third-party version before long, because I don't particularly feel like Dremeling into my overpriced official dock