I think it's a good idea to have an emergency bag. You may not need one for a nuclear holocaust, but for something like perhaps an earthquake it's always good to have around. It can't hurt at least.
That said, I'm a little skeptical about how much use your contents are going to be. For one, you can't know for certain what kind of currency people will be using and for the start at least there will be plenty of regular coins around which won't have been torn apart by radioactive decay.
Now, since I'm on that matter anyway, I wouldn't worry too much about that coat of yours. Instead, get some regular foto film, which hasn't been exposed to light yet. As you may know, when that stuff turns black, you need to start using the iodine tablets (as for drugs: stock up on iodine tablets). Those will at least keep you alive in an atmosphere of minor radiation.
Knives are good for preparing stuff with, but trust me, throw a can opener in there (or maybe even a Swiss pocket knife) and you will be king of all that sealed away food sitting there in the abandonned food stores.
And finally matches, in a Ziploc bag in case they get wet. Their use kind of speaks for itself.
Although on the matter of bags, you may want to exchange your box for one. Since you probably won't want to hang out where ever disaster strikes, something with straps is far more convient to cary with you.
But apart from that, yeah, keep the water in there and (how could I forget) you'll want a first aid kit as well.