From what i understand of tcp/ip packets, the data contained within the packet is encrypted using https connections. End to end from server to requester (you). In tcp/ip theres two parts to each packet, the data and the header. IDK about the header, which contains routing data as to who is requesting the info (your ip), and the server's ip. If thats not encrypted then it would be easy as pie for a middle man to see who is requesting the data from whom (ip addresses), assuming https does not encrypt that data.
If your worried about a man in the middle seeing those ip addresses, which i am fairly sure is not encrypted in https, you may want to consider a VPN. It will route your requests to another IP address through a secure encrypted tunnel that only shows up as random data to anyone watching, and the header data containing ip's is encrypted (i think, but if not it will just be showing your ip and the vpn's ip). The VPN server will send a request to the website in question, and then route the reply back to you, and the header from the VPN server will be their IP and not yours & v/v.
If you trust your VPN provider to not keep records of ip's, then using a VPN is a fairly safe way to ensure your IP is not linked to the requests/responses from the server hosting the website in question. But many ISP's log this data, required to do so by law, but not in all countries.
There's still some bastions of privacy and democracy in europe.
Really though, if they want to know who a particular person attempting to hide their IP is, there is no security gaurd's that will help. There's always ways around these precautions, and at most its makes it more of a hassle, but never impossible for whoever is doing the investigating. And theres always laws (in the us at least), that forces ISP's to cooperate with authorities without warrants in many cases.
Privacy on the internet exists to the extent of the skill/intelligence/power of who is trying to take your right to privacy away, and who is trying to retain their privacy/anonymity. And with high level GOV agencies, they will just use their "brains" to hack/illicitly gain access to data that reveals the identity of who they are searching for. If they really want to find out the face/identity behind whoever they want to, they will.
Take precautions, but always assume that theres no security, because there isn't depending on who's looking. Privacy/Anonymity on the internet is a cat and mouse game, and you have to be proactive if you want to be one step ahead.
If your really paranoid, aircrack/use free wifi access points, a truecrypted netbook with no personal data on it, and a spoofed mac address using a vpn provider you can trust. But once again, thats not foolproof, though its good enough unless you are actively being sought after by people with real power and skills, if thats the case the internet is not for you. Most people don't fall into that category though.
I recommend doing some reading into the tech behind the internet, and the protocols that do all the work for users. Its alot of work, and hard to understand at first, but you can get a rough idea from doing some researching into the subject.
And on a side note, always use randomly generated 15+ character passwords, at a minimum, for anything you need a reasonable degree of security for.
