Only if you can attach a JTAG/serial interface to it, most routers have those pins on the board.
You will need a USB-TTL-UART adapter for it and 3 pins and attach it to the router board.
That is only half of the way, you will then have to check the file system and various proprietary init scripts.
Most routers that are provided by ISPs collect some sorts of data/telemetry, whether you call it a backdoor or not.
A good start can be found here:
However it is not something you should do, and will most likely void your warranty and ISP agreement.
The best way to ensure that your device is safe is using FOSS firmware such as OpenWRT/LEDE, on your own device.