Also: As long as your battery is not dead dead (which, barring the freakest of freak occurences, comes with a lot of warning), just having a jump starter in your emergency kit covers it. Pop the trunk (which can be REALLY annoying on modern cars with only partially dead batteries...), grab it, and jump your car. Bonus points is you don't need to frantically leap into the driver's seat before you crash into a parked car.

To be clear, "an automatic with paddle shifters" (or in general, a manually-shiftable automatic) does not necessarily imply a fancy dual-clutch transmission derived from F1 cars or whatever. Sometimes, like in my automatic-transmission car, it just means you get a + and - on the gear lever and still have a torque converter instead of one clutch (let alone two).

But yes, the one thing that is true in any modern car without a third pedal is that when you push the stick to + or - or pull on the paddle shifters, all it's doing is sending an electrical signal to a computer that mediates between you and the car and decides whether your input will be followed or not. It won't allow a downshift that would cause an overrev (probably in any car, even the most track-oriented ones), in many cases (especially in less-sporty cars) it won't hold a low gear and let you keep the engine at redline but will instead upshift even if you do nothing, and in many cases it won't hold a high gear as you come to a stop and will instead start you off in first again instead of fifth like a real manual would do. And last, but not least, those computer decisions and solenoid activations and whatnot take at least some non-zero amount of time, which -- even if it's a fancy dual-clutch and the total time interval between gear N being engaged and gear N+1 being engaged is way shorter than any human could manage -- it can feel laggy because you give the input and then it acts, as opposed to a real manual where your hand on the gear stick and your foot on the clutch pedal are doing the action to the car directly.