No, this "light blue rollover cable" is for connecting one Cisco-type RS-232 device to another. Most usually, one device was a PC serial port, with a great adaptor (9-pin female D-type to 8-pin female RJ-45), and the other is a Cisco console.
Given that most computers now don't have serial ports, you normally get a USB serial with a light blue cable on it. (search for "USB Cisco console cable" .. it will be a USB-A plug at one end which goes into your laptop, and a RJ-45 plug at the other, which goes into the console socket of the switch. Inside the cable is a USB-connected serial port, which shows up as
/dev/ttyUSB9 in Unix and
COM9 in Windows. (Your
9 will vary.)
Although it's possible to find ethernet to serial adaptors, they are unusual and somewhat complex.
The USB version will be the cheapest and simplest solution.
NB: Do check the console port socket on the switches. Some are not the familiar Cisco console RJ-45, it depends on the exact switch model.