Yes, actually. I don't think you understand just how pervasive Google's presence is on the internet. Install Ghostery or similar sometime. Then watch where Google Analytics shows up. This will be some rather surprising places, including porn sites and things you might find yourself feeling rather sensitive about.

Remember, not only does Google have records of every search associated with your IP, but they've spent a lot of work trying to differentiate and distinguish people as their IPs change. They also index all email you receive using their services or if your place of employment uses those services.

In sum, this is actually a very detailed picture to paint of someone. It's not a matter of simply not using Gmail or Google, they've infested the internet with bugs that still provide detailed information of where people have visited and it's actually a bit of effort to slip under their radar. More effort than the average person will ever spend, anyway.

And it's not like you can have them remove what they already know about you, you just have to write that off as a matter of record now. If you still think this is a good thing to hand this all over to a company that owes you absolutely nothing and whose existence largely depends on holding this information about you...