It's likely that 1A will be too little. As you may know, the USB 2.0 standard limits output to 0.5A. The way USB is supposed to work is that each device asks the host for the amount of power it needs and the host is responsible for either granting or denying those requests based on the available power.
However, there are many devices which simply don't actually follow the standard. Paradoxically, this means that well-made and well-engineered USB hubs that actually do follow the standard will not be able to supply enough current. Devices that don't follow the standard may or may not. There's no way to tell because ... they don't follow any standard.
With that said, many dumb "wall wart" style chargers omit the active host hardware and solely supply the +5V for charging or powering phones or other devices. They don't actually do the negotiation phase and simply put out power. The way voltage regulators in such devices are typically designed, they will put out a steady and reliable 5V until they get near their rated design capacity, usually specified in amperes (A) or milliamperes (mA). Cheaply designed and built devices will start to let the voltage sag before they get to their design capacity. Better designed devices will hold their voltage all the way to their rated capacity.
So with all of that, you're better of powering your RPi 2 with a "wall wart" style power supply that is rated for 2A (2000 mA) or more, and then only plugging the USB devices you need into the Pi. If you need a powered USB hub (as I did with my Pi Zero), I'd recommend powering it and the hub separately.
A note of caution
Normally, in a working USB connection, the power flows from the host to a peripheral device. So, for instance, your USB keyboard draws its power over the USB cable from the Raspberry Pi's USB connector (assuming they're connected directly together, as they are with my Pi2.) However, the current isn't supposed to flow the other way. That is, USB was not designed to have your keyboard power the computer it's attached to. In fact, the USB standard is pretty clear that this should be actively prevented by including a diode in the case that the external device is powered by anything other than the USB connection itself. In other words, a properly designed USB hub will not allow current to flow from itself toward an attached computer -- only the other way around is allowed. Electrically, the device that accomplishes this one-way flow is called a diode and it only allows current to flow one way.
Unfortunately, as mentioned here some USB hubs are not equipped with a diode to prevent reverse current flow. (They probably figured they could save $0.05 and so it was worthwhile.) However, that can mean that if there's a power failure for the Pi but not for the hub, the hub will "backfeed" the Pi. This isn't necessarily fatal, but the Pi is not designed to take its power from the USB port and so backfeeding it that way bypasses the voltage regulation (and voltage protection) built into the Pi. The result is that as long as the voltage is 5V, everything will be fine, but if the voltage goes too far above that, the Pi has no defense and damage may occur.