Yes, FD7 opens files written in earlier versions.
Open an FD5 / 6 file the way you would open an FD7 file -- no additional steps are necessary. Go to File > Open and select the script from your hard drive.
Open an FD4 file the same way you would an FD6 or FD7 script; the difference will be that the program will place the word
in the file name. Resave the file with a new name (File > Save As) to create a separate FD7 file. Make sure you've removed the (converted) from the file name. Continue to work with this new file and not the old one.
For FD2 and 3 (Mac only), you will need to use Microsoft Word's Recover Text from Any File command. Instructions are HERE.
NOTE: Live support for Final Draft 7 has been discontinued. You will still be able to install, activate and use FD7 on appropriate computers but email, chat and telephone support is no longer available. Live activation assistance is still available via phone (818-789-6281) and email and chat (links on the left side of this page).