Yes. This is a straight-forward process that you can setup independently, and our support team can assist you to setup.

Among other reasons, some people want to be able to switch out of threaded conversations, which you can do simply in the Zimbra web interface, and many people want to be able to use IMAP to sync mail with their mail client like Outlook, Mail.app, Thunderbird, and the like. Other differences between Zimbra hosting and Google Apps are listed in table form here.

There are a number of ways for you to use Google Apps and 01.com Zimbra hosting together, here are some:

1. Order Business Zimbra Hosting: use a new host for your domain name, such as 01.yourcompany.com
2. Setup the MX records for 01.yourcompany.com just the way you would for any new domain, follow our instructions
3. Use the domain admin to securely add mailboxes at which you will receive mail from respective Google Apps accounts
4. When adding mailboxes, use the canonical address field to change the "from" address for your users to your regular, yourcompany.com domain, so email you send from 01.com will appear to be from your accounts at Google Apps
5. Use the Zimbra Identities feature in the Options tab for each user to further customize and add options for sending "from"
6. Set your respective mailboxes at Google Apps to forward to your new mailboxes at 01.yourcompany.com
7. Setup your desktop mail clients such as Outlook and Mail.app to securely IMAP to your 01.yourcompany.com accounts
8. Set the "reply-to" addresses in your mail clients, if you're using them, to reflect your yourcompany.com addresses

For your reference: Zimbra forums post on the canonical address field in the mailbox setup window.

You may also use a personal or business 01.com Zimbra hosting account with Gmail. You may use the forwarding field in your Options tabs of your Zimbra mailbox to define forwarding options, such as to your Gmail service. This way you can synchronize Outlook to the 01.com Zimbra account, yet still keep your Gmail account.