There is no warranty that your child will be protected by the seat. The warranty is only for things like lockoffs breaking, covers fuzzing, harnesses fraying due to normal, everyday use.
Every manual specifically has a disclaimer that not every crash is survivable, even with a properly used seat. The seat is not guaranteed to protect your child from injuries.
Now, in very rare circumstances, there have been lawsuits filed and won where the case was that the child restraint failed or was improperly designed.
In your everyday crash, a different cover shouldn't make a significant difference. The big thing about using original covers is that it is designed to properly fit your seat, covering what needs to be covered (like foam) and not covering what shouldn't be (like labels), it has the airbag warning label on it for RFing seats, and it has been tested to meet flammability requirements. If your vehicle caught on fire and your child was burned, using an aftermarket cover would mean that your child would sustain worse injuries.
Other products are more likely to cause injury in a common crash. BundleMes are too bulky, and introduce slack into the harness, increasing the likelihood of ejection. The MightyTite (1) stretches out the vehicle belts, so that they can't stretch like they are designed to during the crash, and (2) you can get the belt SO tight with it that you can damage the belt path of the carseat.