Yes, the start of boot results in output to the serial console, so if your device listens during that time there is a strong possibility that it would also reply (which is a mistake that would halt during u-boot stage).
All steps to work around this are essentially the same…stop a keystroke from appearing during u-boot stage (even if it isn’t really a keystroke).
One method you’ve thought of already…edit u-boot itself and remove its serial console function. Probably not a good idea, and not easy.
Another method is to disable the COTS device until something triggers connecting it. An example would be using a GPIO which would only assert upon kernel load (once kernel loads it’s easy to disable serial console function simply by not adding the option in the command line in extlinux.conf). The GPIO could be used to enable the power going to the COTS device.
If the reboot can be sensed in any way, then you could simply put a solid state relay in with a short delay upon detecting power, e.g., 5 seconds.
There may be something in the u-boot environment which can be set to disable halting to u-boot command line, but I do not know what it is (or even if such a thing exists…it it does exist, then this would mean extlinux.conf is your only interaction with u-boot other than flashing once that environment is set up).