As far as the whole discussion about what waders do once you do go in, on forums like this (I spend more time on fishing sites, but it's the same debate everywhere), the answer isn't quite so simple as "yes, waders drag you down" or "no, waders don't" (and in the case of neoprenes, we might also add "no, in fact they float you").
It's important to remember that when we're talking about how you maneuver on land, we're talking about weight, but once we're in the drink, we're no longer talking about weight, but rather density, more accurately, density compared to water. I guess to be strictly, technically accurate, we're also talking density on land too, but air has a density so low that for our discussion, it's practically negligible.
Anyway, this matters because in a 'falling in' situation, both scenarios are at work. Part of you is in the water, and part of you is in the air, and you're desperately trying to get more of you in the air than in the water.
At this point, your waders are filling with water. This means that this water is effectively becoming part of your body, along with your clothes (which are likely soaking up water) and your waders (which aren't, and if they're neoprene, actually have air trapped within the material). This changes how 'your body' (that is, your body including clothes, waders, and recently borrowed water) will behave in the two environments. For the part of you in the water, there isn't going to be much difference from swimming normally, since the water added is exactly the same density as the water outside the waders. It's going to make it a little more tiring to swim, but only slightly so. It's once you start to get back out of the water that things get much tougher, as the water in your waders gets picked up above the water level of whatever you fell into, and suddenly, all that extra weight is up in the air, pulling you down.
With waders full of water it's actually way, way easier to swim to shore than to walk around on dry land, as the water can add a surprising amount of "body weight", but only when it's out of the body of water. The water that your clothes soak up only add to this as well. To sum it up: waders full of water will tend to keep you at the surface of the water. If you sink, it'll be barely more difficult to get back to the surface in waders than it would be if you were swimming in shorts, but when you try to improve your situation and get out of the wader, the full waders will turn into a heavy anchor keeping you in (but not under) the drink.
It's also worth keeping in mind that none of this accounts for the shock of cold water, and these effects are just as applicable in August as in January. This cold is something that's difficult to prepare for, and while I've never gone in completely (swimming) in sub-freezing conditions, even getting waders filled to the knee in those conditions will take your breath away. If this happens, consider your hunt over. Even if you're okay, you absolutely need to get dried off and warmed up. If you're a long way from your vehicle, pack up and move out immediately, as you don't want to wait out there until adrenaline wears off and hypothermia has sapped your strength, energy, and mental sharpness. The process begins as soon as you feel that shock of the cold water, and it doesn't stop until you're dry and warm.