This is a difference between Firefox and Google Chrome: you don't actually sign into Firefox itself, and your Firefox Sync account, if you set one up, has its own login separate from your Google account. Firefox does not sync with your Google account (it's not a built-in feature, it would require an add-on).

However... if you sign into your Google account while using Firefox, then Google can associate all of your usage of Google services in Firefox with your Google account, just like it can in any other browser.

So if I went into incognito, and clicked one of my bookmarks, will any data from the site be stored by my Google account?

So if I went into incognito mode and clicked on one of my bookmarks, will the data be stored by my google account?

Firefox has private windows, similar to Chrome incognito tabs.

Your private windows do not inherit your Google cookies: they share a separate cookie jar. So if you do not log in to your Google account in the private window, then it will be difficult for Google to track your activities (for the most part, you will look like a random user instead of a known user).

I say difficult instead of impossible because if you enable Flash, then sites can store and access "Flash cookies" which I don't think Firefox can separate between regular and private windows.