You're confused, son.
If you are wearing waders, no, your feet will not get wet. That is, they're not supposed to get wet. If your feet get wet, your waders are leaking. Doesn't matter if you're wearing neoprene or breathable -- no water is meant to get inside the waders. Now, if you're wearing "sock-foot" waders with a tie-up boot, then water will get into the boot, yes, but your foot will be inside the sock-foot of the wader, so, again, if you've got waders on the only part of you that supposed to get wet is your hand when you're catching a fish.
There are generally two kinds of waders -- neoprene (reminds you of a wetsuit) and breathable waders (pliable fabric that basically looks and fees like waterproof clothing fabric).
Most breathable, sock-foot waders come with a neoprene sock because it's comfortable and form-fitting and it takes punishment. It used to be said that neoprene waders were better in very cold water but that's not really true anymore. Neoprene was only a "warmer" option because they're thicker and provide more insulation, but it can also get quite clammy under a set of neoprene waders, which can serve to make you colder. Multi-ply breathable waders are very warm nowadays, and with a pair of thermals underneath you'll be warm AND comfortable, because they don't constrict movement and they don't trap sweat and moisture side (that's why they're called breathable).
My favorite boot is the Simms Freestone. I've had a few different wading boots (including an old pair of hiking boots) and these are the best I've ever had. They're non-felt sole, feel good to hike in and seem exceedingly rugged (only had them since winter, so, they still look brand new). They cost $129, which may be more than you wanna spend, but if it meets your budget, I'd get some:
http://www.flyfishingoutfitters.com/onlineshop-wading_boots_sandals-simms_wading_boots_sandals-simms_freestone_wading_boots-simms_freestone_boot_vibram
Edit -- I didn't down-thumb the previous answerer. I disagree with him about the neoprene thing, but otherwise his answer makes sense... gave him a thumb-up. All this down-thumbing is a bit outta control, y'all...