If on Wifi only, how does Mail work when not connected?
Yes. Email works well when not connected to internet.

You will get warnings that it cannot connect to your email accounts. One warning pops up for every email account that you have set up on your device (and possibly one for all the outgoing servers as well). After canceling all of these, you are home free.

If you send an email and are not connected to the internet, it will sit in the outbox, and should send automatically as soon as you reach wifi connectivity. (It may alert you that it failed to send.)

Like you thought, there is an icon that appears for any attachments that aren't downloaded. If you aren't connected to the internet, you won't be able to engage the download of the attachment.