Sure you can. Set it up as Range Extender mode.

I was sure I can. I asked it here to be 100% sure, because this friend of mine that wants to enable the configuration, was given an answer by someone else that the Ethernet port of WA730RE was only for setup use or something like WAN. He was so definite that suggested my friend to buy another device (like TL-WA701ND) instead of WA730RE to do his job. What do you have to say about this opinion?

100% sure. I have an extender TL-WA830RE which is hard wired to my desktop. And it works perfectly.

Hi;
You can definitely use WA730RE for your solution. Also TL-WA701ND works perfect in this solution. In my opinion TL-WA701ND is a better solution because it can works under client mode. Consider that client mode is the answer of your question.
"the DEVICE will be connected on the network wirelessly (on a modem/router), and the computer will connect to the network from the Ethernet port of the DEVICE with an Ethernet cable"
This device is an access point with client mode.

The range extender also repeat the wireless signal that have benefits in some solution but in your solution its better to focus the power of the device on getting the signal from the wireless network.

GOOD DAY and happy new year!