can icloud backup emails sent to a gmail address?

When you write and send mails from iCloud.com say in Fom field : the mail address is example1@icloud.com and recipient mail address is example2@gmail.com the mails can be archived in iCloud.com

See the articles Write and send email in Mail on iCloud.com - Apple Support

Archive email in Mail on iCloud.com - Apple Support

The second way is move those mails in a folder created see the article Organize email with folders in Mail on iCloud.com - Apple Support