In short, it tightly links email, browser, and computer as a singular identity. This can be a good thing, for example, my netbook (soon to be Chromebook), Nexus 7, and Samsung 4 are only used by me, so its great having my bookmarks, history, and settings synced across devices.
School is different, as we have been told they are workstations with multiple users. While in a perfect world it would only be one person on a desktop, we all know there may be times a student or staff may use our devices.
This year it seems that sync is more forced so I want to describe the consequences of syncing Chrome with your district account. At this time I would caution against syncing your MMSD account. The two big consequences is the loss of Incognito Mode in Chrome, and the loss of ever syncing your MMSD account in the future. Incognito Mode is private in the sense cookies, search, and history are not stored. You may use this to check social networking sites or secure banking transactions on your lunch hour. On a multi-user devices Incognito Mode is essential in keeping users personal information private. Last year in lab 4/5 students were encouraged to use Incognito Mode for Gmail transactions. Another big issue is if you use the district sync you will forever lose the ability to sync with another email address.
I would suggest avoiding MMSD sync at this time. Here is what you need to look out for. Selecting Sign in to Chrome after you are logged into Gmail will begin the process. As long as you don't sign into Chrome you should be fine.
If you do select the MMSD sync this warning comes up.
Important information regarding your Chrome data
You are signing in with a managed account and giving its administrator control over your Chrome profile. Your Chrome data, such as your apps, bookmarks, history, passwords, and other settings will become permanently tied to firstname.lastname@example.org. You will be able to delete this data via the Google Accounts Dashboard, but you will not be able to associate this data with another account.
Learn moreIf you prefer to keep your existing Chrome data separate, you can create a new Chrome user for email@example.com.
I think for most staff and students it is best to avoid the syncing of data entirely. This is specially true if the computer is a shared device. Not only does your account become tied to that computer but you lose the function of Incognito Mode.
If you are someone who is the only user of your computer and you need access to your account at home, syncing could be an option, but I still would not go the MMSD route for above stated reasons. What I would do is create a separate Gmail account for the sole purpose of syncing. After the account is created and before you log into MMSD Gmail sign in to Chrome using your new Gmail account. After that log into your MMSD Gmail and you should be good to go.