There's some good info on the internal circuitry of LED strips here. You will see that any practical LED strip design will include internal current limiting (usually just a series resistor) such that a 20% overvoltage shouldn't be a problem.
But you should also Google for "AAA battery voltage vs current" and read some of the references, so you'll understand better the realities of battery application.
You will see that 2A is far beyond the maximum current a AAA battery can supply, especially for any practical amount of time. You will also see that the output voltage of a battery depends on the current you draw from it, because the battery itself has internal resistance, that battery voltage declines with discharge for most types, and that even the initial voltages are only nominal.
A "1.5" Nickel-metal-hydride battery's actual voltage is only about 1.2V, a perfectly justifiable falsehood because the voltage of an alkaline "1.5V" battery will fall continuously throughout its life, and any circuitry properly designed to run off them will be designed to work even when they're down to less than 1.0 volts.
The output of a nominal "1.5V" lithium battery such as the Energizer L92 (Google its product datasheet) will be 1.8V when new, drop quickly to 1.7V if lightly loaded, or to 1.5V if you draw 100 mA from it, and will steadily decline to about 1.3V at end-of-life (where you've drawn about 1300 milliampere-hours from it). Trying to draw 2A continuous current from an L92 would probably cause it to explode and start a very nasty fire.
It's really important to get and read battery datasheets, especially for any heavy-load application. A bomb is in essence a container of chemicals whose total potential reaction energy is released in a short time. A battery is a container of chemicals designed with the assumption that their total potential reaction energy will be released in a controlled way over some extended period of time. Overloading or short-circuiting a battery turns it into a bomb. (The same applies to any energy-storage device.)