I assume you mean if you put an old hdd into a freshly installed Win 10 build then it depends, if the games were installed via a launcher like steam or uplay then no it will not just open up. You can try to install it through steam again and try to link it to the directory the game is already in, that way it'll identify the game files and not install it all over again.
Or if it's a stand-alone game that does not require installation then you should be fine. But any games that required a formal installation will not run without special configuration or at all.
This is because when a game installs it writes certain information to windows registry that tells windows where to search for those specific files. Without this windows won't...