I found the Orcish Boots of Muffling inside a chest earlier, and the description says something along the lines of the boots silencing my footsteps. Will my Sneak skill continue to increase normally while wearing them and sneaking? Or do they provide some sort of perfect, totally silent sneak that I don't learn anything from?
The Muffle effect (whether from enchanted boots, the spell, or the perk) does not increase your Sneak skill, but rather it reduces the chance that someone will hear your noisy armor (by making it less noisy). Thus it does make it easier for you to sneak while wearing armor, but not by increasing your Sneak skill (for example, you're still just as easy to see as without the boots, you're just harder to hear when you move).
Exactly how this mechanic works is, as @yx mentions in the comments above, not exactly clear, especially how the hidden magnitude of the effect comes into play (if it does at all).
If your question was intended more along the lines of "Can I still level Sneak while wearing them?", the answer is of course, "Yes" -- any time you are sneaking and hidden (and there are people around who might detect you) you gain experience in Sneak; the Muffle effect makes it easier to succeed at sneaking, which makes it easier to level the skill, but does not directly impact your leveling of Sneak.