Copying To Local Folder versus Downloading Offline Use

I created an imap setup with Gmail.
I have a label that I wish to delete most of the messages on the gmail server, however I wish to retain them as a backup on my pc.
If I download them for offline use then if I delete it on gmail it will also be deleted in emClient
If I copy the folder to a local folder without using the download for offline use option, will the full messages still be copied to the local folder? 

As a 2nd part to this question, I notice by default images are not downloaded.   So if I migrate emails from a label/folder to a local folder than delete the original, I still will not have the images.   I don’t want to download images on all emails because this will take too long.   If these images are only url based and can be downloaded anytime, even after server email is deleted I am ok with this… understanding that the sender may eventually delete the email from the source url when it is outdated

Sort of a mess.   Moved thousands of emails from imap folder to local .   Got an error that it could not connect (my connection was fine).  But now my emails are in neither folder in em Client.  They disappeared.  They are still on the server (not even resyncing)_ but does not boost my confidence in this program.

If you copy messages from an IMAP or Exchange folder to a Local Folder, the complete message content will be downloaded and stored on the computer. This does not depend on the IMAP settings you are using for offline availability. Local Folder messages will include all attached or embedded images or other files. Linked images will always require a connection to the source to display them, as they are not included in the message.

It may be that there is some corruption in the message cache. Right click on the folder and choose Properties > Repair. This will re-sync the folder with the server.