Not necessarily. A site could quite easily just show you a pre-generated address from a list of pre-generated addresses which all belong to a malicious attacker, regardless of what private key you enter. Downloading the site and running it offline won't protect against that at all.

If you are going to go down that route, then you should use multiple sources to make sure that they generate the same address, and the sources you use should be open source. Ideally, the computer you enter your private key to should be permanently airgapped rather than just temporarily offline. If you don't have an airgapped computer, then a run a live OS from a USB stick. You could download and verify Electrum from electrum.org, as well as an open source site such as bitaddress.org from their GitHub, and ensure the address generated by each service matches.