Your correct that the Remote does not recieve anything back from the TV, however most IR Adaptors like the picture have the ability to send data as well as recieve as there designed to communicate with other devices (i.e. mobile phones, old HP PDA's) that have the same style adaptor built in.
I suppose it depends on your level of willing to DIY / tinker with the IR Adaptor if it does not work out of the box for what you want..
Just having the adaptor installed in your PC will not give you any control over the PC, as it depends upon what the software that came with the IR Adaptor is capable of and if its able to understand the signals being sent from your remote control.
Before spending any money i would check that the IR adaptor your going to buy supports your TV remote, then do a bit more digging about the adaptor to find out what software if any it comes with and what that software is able to-do.
I would also have a look on google for anyone else that has done a similar thing with one of these adaptors, read into how they did it, what if any software they needed etc, the best thing to-do then is try and mimic what they have done, or at the very least get the same type of adaptor so you know that at the least will work for you.
Hope this helps.