The UART adapter board will fry before your laptop. And if you're connecting it correctly, you shouldn't fry anything. Even if there is a picture with information on connections, I have gotten in the habit of verifying Vcc and GND on the router end with a multimeter. RX and TX are trivial, and I tend to not make connections with the router powered up, if I can help it. A proper header with pins and connector for the adapter cable are ideal, but.
I wasn't confident because it was the first time I had attempted something like this. I did have pins and all the right cables.
It was good fun trying to un-brick the TP-Link but ultimately I messed it up but it was only a cheap router. It gives me an excuse to buy something else, possibly an Asus AC-88U. It's router heaven around here, so much choice.