No they wouldn't. That kind of retarded attitude is what causes power creep in MMORPGS. Everyone wants "balance" but nobody wants to see their favourite thing nerfed. It makes no sense. If a problem needs solved, you solve it. you don't readjust everything else to create an environment suitable for the problem to live in.
+ init when unarmed (cause you get +3 with a dagger, you should have +5 without!)
It doesn't make logical sense to have a bonus for doing nothing. A human, in their natural unarmed, unenchanted, unarmoured state, should have no bonuses to anything. It doesn't make sense to have an initiative bonus while unarmed, where is this iniitative bonus coming from? This is what base values are for. I suppose you COULD increase the base initiative value, but give all weapons a penalty to match (even daggers would have to be negative to satisfy your logic). However i don't think this would be correct to do.
The logical explanation why a dagger or sword would give you initiative (thus making you faster by using them) is reach. With a sword, your arm is effectively twice as long, meaning that you can strike at enemies without stepping forward and putting yourself in more danger, and thusly also having less recovery afterwards.
Using a dagger is essentially identical to being unarmed, but with a pointy hand. The sharpness of a dagger means that you don't need to use as much force as you would when punching, and you can focus on moving more quickly.
+ init and dodge when lightly encumbered (<40%)
- init and dodge when heavily encumbered (80%+)
given the aforementioned logic, pure penalties are the only thing that makes sense. It's illogical that wearing armor would speed you up, yet wearing a little too much would slow you down again.
Yes penalties to dodge make sense even when people have zero dodge already. IT just goes negative and ADDs to the enemy's accuracy rather than reducing it. This makes reasonable sense, as it's a lot easier to hit a statue than a person, it doesn't move. The slower someone is, the easier they are to hit. Even a cowardly newbie who doesn't know his sword very well, can hit a statue.
As to strengthening the penalties, I think it would make sense to adapt some abilities. For example, the Dodge I-III traits, could be changed to only apply their effects when the champion is <50% encumbrance, so the penalty would be losing some of your existing abilities, rather than stacking on a flat amount which may or may not fully counteract them.