Updating Exchange 2013 CU1 to CU11 Steps

Is this stand-alone or you have DAG?

It will probably check to see if you have met the preflight check before it installs.
The rollups on the Exchange boxes are finicky.

If it appears in the update folder on the server then,run it that way.

Otherwise you will probably need to run it as a standalone from an elevated command prompt with ACU turned off.

Standalone server.

I am trying to find out all the downside of doing this as we need to communicate this with our client before having do such a huge update that might break their server if it goes all wrong.

Yes, that is totally right, you need to be ready for worst situation or we say back out plan in change management. This is what you need to do:

1) Take Server backup. Both AD and Exchange.
2) Upgrading schema, your AD admin will know it. Else, if your ID is part of Enterprise, schema and Domain admin, setup will do it automatically.
3) If you have any OWA customization or any 3rd party tool, note down all settings, as that might be overwritten by new update.
4) Now you can start the CU installation. However, run the setup in admin mode.

For more info, check this:
http://exchangeserverpro.com/exchange-2013-installing-cumulative-updates/

Now, in case you have any issue and you need recover it back. Follow this:
https://technet.microsoft.com/en-IN/library/dd876880(v=exchg.150).aspx

We are the admins for the server. I never done a exchange update that requires a AD update schema. Will the update itself just do it or will it STOP and tell us what needs to be done or are theri steps for schema updates.

What's your backup software?
I usually take an image of my server and run a virtualized instance and apply patches to see what breaks.
Beats the beejeeez of of trying to restore a production server if M$ does it's usual high qualty patching job.

backup exec but dont have a way to really virtual the box.

Do you know how long it will take to run the update?