My gut feel (personal experience, not research) is that the whole of the icons' nature is important. Them having simple shapes doesn't necessarily solve the problem and could in some cases make it worse.

Imagine for example a set of icons that are monochrome, open-ended glyphs comprised of a single stroke with line weight similar to that of the text. This could complicate visual parsing greatly due to high visual similarity to text.

On the other hand, a 16px checkbox control with subtle gradients, shadows, and depth cues looks absolutely nothing like text and is filtered out by the brain almost automatically (unless of course the checkbox state is pertinent to the user's intent). Same goes for a 16px colorful icon with shading like used to be ubiquitous in desktop operating systems.