No, the Visible universe has an edge, as defined by the age of the universe in light years.
That too, of course, but the distinction is subtle to the average person. The Visible Universe is pretty much time-dependant (once a certain limit of enhanced visual acuity has been attained) and is therefore edged by the speed/transmittability of light, while the Known one is governed by the sum total of information gained from various emperical and experimental analyses and observations (and maybe a little assumption that may be proven wrong) and thus is transient and ever changing as long as advances in understanding. Give or take.
Although I tend to think of the Known universe being edged by a 'crinkly' pattern down near the Planck level of detail, and an interesting part of its boundary being in the future (e.g. we know that the Earth's orbit is stable for a given amount of time, assuming Sol itself doesn't do anything crazy, but we're not sure beyond that), as well in the (literally) distant past, where might be congruent, though not sat on top of each other, in the the Visible one you mention.
@Andir: not sure I would agree at your simile, but I suppose it could be adapted into an analogy instead.