There isn't a way to pin the Library Browser window, but there are several ways to quickly access the library contents.
You can quickly access the library browser by choosing Library Browser in the Window menu or using the shortcut Ctrl-L on Windows (Cmd + L on MacOS). The Library Browser window will reappear with the text cursor in the search field.
In PLECS 4.4 and above you can also use the quick access feature that lets you insert components in a schematic window without having to change to the Library Browser window. Single click in an empty portion of the schematic and start typing your search query.