The car battery is in fact comparable to a large capacitor. It does have impedance, especially as it ages, but it's the impedance of the wiring that's the worst culprit at high frequencies.
A capacitor will often not help at all, because it will primarily only shift the frequency at which the transient will ring. It may well reduce the maximum voltage (or not), but it will not reduce the energy available by much. It's very difficult to characterize the impedance of the system you are placing it in, making it just as difficult to predict the results.
A transient suppressor would be a much better choice, as it's designed to both limit the maximum voltage and absorb energy. If you could put some resistance between the transient suppressor and the LEDs, even better.
Maybe the worst thing that is somewhat likely to ever happen to your LEDs is to get a jump from your friendly local tow-truck. He has a 24 volt system and heavy cables with strong clips, and will raise the voltage of your electrical system way over 14.4V. Any component or system installed by an OEM or sold by a reputable third party is required to survive this. I forget exactly what the spec I'm working to right now says, but I think it's 26 volts for 5 minutes. I was more concerned with the 76V load dump the spec says it has to survive, even though this is an event the vast majority of vehicles will never experience.
Also, you need to understand that just because the typical voltage of your LED is 3.6V does not mean you can run it at 3.6V without any trouble. That's right. If you connect a 3.6V (typical) LED to a 3.6V supply, you may substantially overdrive the LED. Or you may substantially underdrive it. Unlike a regular light bulb which operates at a fixed voltage and draws as much current as it wants (a big rush at the beginning followed by a rapid settling down to a relatively constant value), an LED should be operated at a fixed current, and will settle at whatever voltage it wants.
The specs mean that if you put the rated current through it, it will typically settle around 3.6V, but it could be higher or lower, as low as 3.2V in some cases. If you have a case where rated current would result in a voltage of 3.2V, or even 3.4V, but you apply 3.6V, the LED will draw well above rated current. Unlike a light bulb, where a 10% increase in voltage results in less than 10% increase in current, in an LED a 10% increase in voltage results in substantially more than a 10% increase in current.