The problem with the attack as you're describing it is that it's glossing over a lot of details about how keyless entry and start systems work, and details about built-in backup systems, some of which have been covered in comments on the question and other answers.
First, let's cover getting into the vehicle: In other words: could the attack described in the question function as denial of service in the sense that it would stop you from entering the vehicle?
- Manufacturers of automobiles understand that active electronics are prone to faults, and hence they design workarounds. For instance, key fobs provided for remote or hands-free unlocking of doors typically include a backup physical key, which can be used in a backup keyhole in the door to open the vehicle if it is locked. So, an attack designed to disable the rolling code process of authenticating the key would not stop someone in possession of the key fob from getting into the vehicle.
- Further, some keyless hands-free transponders (ie the variety that unlock the door when you touch the door handle) work on bidirectional communication, so once again a rolling-code-disabling attack wouldn't stop you from entering the vehicle.
Now, let's cover starting it once you're inside: Could the attack stop you from starting and driving the vehicle once you were inside?
- Vehicles with keyless start (ie a "push to start" button) work with bidirectional transponders, not rolling codes - the starting sequence includes two-way communication between the vehicle and key. So, an attack designed to disrupt rolling code generation would not stop someone in possession of a functional key fob from starting the vehicle once they were inside it.
- Further, vehicles with keyless start typically include a passive starting mechanism, designed to allow you to drive the vehicle in the event that the active electronics in the fob have been disabled. (for instance, if the battery dies). These systems are typically meant to be "idiot proof" and not involve complicated procedures - typically, you hold the fob itself against the start button, or you hold the fob against a designated spot on the steering column (both of which which nicely mimic the old-fashioned method of using a physical key), or the backup physical key you use to enter the vehicle also works in a hidden keyhole on the steering column. So - once again, even if the active electronics are disabled in the fob, as long as you have the fob, you can still start and drive the vehicle.
- Cars with fobs always have procedures to re-sync a new (or disabled) fob to the vehicle. These procedures are designed to allow an owner to sync a replacement fob, ie in the event that their original fob(s) have been destroyed or lost. Sometimes, these procedures are complicated, and sometimes they require some sort of backup authentication mechanism - ie you need to have another working fob, or you need one of the built-in backup keys from a working fob, or you need a brand-specific diagnostics tool plugged into the vehicle. This makes things inconvenient for sure, but as a last backup against the above-mentioned points, it would still let you operate the vehicle if all else failed, and you remained in possession of a fob that had somehow been un-synced from the vehicle.
So - in summary - if the premise of the question is,
Can I perform a denial of service attack - ie, prevent someone from using a vehicle - with an attack designed to disable the rolling code feature potentially used by the fob to authenticate with the vehicle?
The answer is pretty much no that won't be an effective denial of service attack.
If, instead, the question was,
Can I make it annoying or difficult to use a car by disabling the rolling code feature in the key fob?
The answer is probably yes although this is somewhat subjective. If you have a friend who isn't very "aware" of how their vehicle works, and doesn't understand the backup features, and is out of their wits because they've been drinking, then yes - this would probably be an effective denial of service attack. But so would removing the battery from the fob, which is probably easier and quicker than button-mashing a few hundred or thousand times. And it's definitely easier and quicker to just take their keys.
As a final footnote, if the question was meant to include aftermarket alarms/security systems installed on vehicles, I think it's safe to say all bets are off since there have been a variety of such systems over the years that work (or don't) in all kinds of different ways - some of which are just as destructive as poorly designed antivirus software, in the sense that they cause loss of use just as much as they prevent a perceived problem.
If the question was meant to include garage door systems, then - yes - it will basically work, at least against older, simpler systems that had a button-mash potential that was reasonable (hundreds, versus tens of thousands). However, it would still likely only be an inconvenience, as most garage door systems also have backups - ie, the homeowner can enter through another door, make their way into the garage, and pull the manual release handle on the door's drive system, which decouples the opener from the door and allows the door to be opened by hand.
