Yes. A Google profile is only necessary if you want to share publicly or use Google+. A profile helps you communicate with the people you know from a variety of Google products — for example, sharing driving directions from Google Maps or sharing a video from YouTube. Your Google profile lets you control the details you share about yourself, not only on Google+ but through services like Gmail and Web Search.
You do have the option to delete your Google profile at any time. After you’ve created your account, you can remove your Google profile and associated Google+ features through My Account. You can also download your data, including your profile, photos, and contacts, to your computer if you want a copy of it.