That’s not how computer files work. My Computer on Windows XP, Computer on Vista/7/8/8.1 and This PC on 10 are not folders.
If you have a folder simply titled My Computer and copy it to My Drive, you will only put a copy in the cloud. Any changes made to the local copy would only be made locally and would not be reflected in the cloud copy.
Just move your data to the cloud and work with it there. Make a conscious effort to keep copies of your data updated in at least two places, but don’t lose control of your data by accidentally fragmenting your data sets.
If you use the backup feature of the Backup and Sync tool, it will keep the most recent version of your files backed up to the cloud. It works for what it is, but many dispute whether it’s a true backup. I think it’s better than nothing.