Mac Mail - Stagger / batch download emails from gmail over imap
Assuming you are using Mail.app included with OS X, there is no built-in way within the application itself.

There are other approaches.

Lower Your Internet Speed

However, you could artificially limit the speed of your Internet connection while the initial synchronisation takes place.

You can limit your Internet connection using Apple's Network Link Conditioner. See the NSHipster article about how to get and set up this useful developer tool:



Using this approach will allow you to run Mail continuously without risking your IMAP access being limited.

Manually Enable and Disable the Account

You could add the mail account, then manually enable and disable the account as desired.

Mail.app > Mail (menu) > Preferences > Accounts > Enable Account (checkbox)

You can measure the network traffic using Activity Monitor.app's Network view; see Sent Bytes and Rcvd Bytes.

Applications > Utilities > Activity Monitor.app

This would allow you to watch the initial synchronisation traffic climb to a reasonable level before disabling the account.