Yes, you can add the same account to multiple devices. You can even have more than one account on a single device. I personally use my Google account on my Verizon phone, 2 Wi-Fi tablets, 2 Wi-Fi phones, Google TV and several computers. All synced and works perfectly.
I'm going to expand on my answer a bit as it originally just said "yes" but didn't explain...
Yes, you can use a a single Google account on multiple devices. However, if you're looking to consolidate emails I would actually suggest still having separate Google accounts for each device to save settings and other personal preferences but then add the joint Google account just for shared email use. It's always good to have a "backup" Google account as Google's security features send alerts to other accounts. If you only have one account, someone can hack the one account and you would have less options for locking them out and getting it back.
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To set up multiple accounts on your Android device, you would first set up your personal account as normal-- you probably already have this set up from when you first powered on your new phone and entered your Google account information. Then you can go into the phone's [Settings] and [Accounts] and press "Add account". On my Android 5.0 Lollipop, "Google" has a green dot next to it showing there is already a Google account set up, but you can just tap it again and add another Google account. Make sure when it asks to back up phone settings to decline-- keep that stuff separate and personal. Then, still under [Accounts], tap on the new account and change all the sync settings so just Gmail is synced (or anything else that you want to share- perhaps Keep notes or a shared Calendar).
That should do it. You can even go further by managing your labels in Gmail to filter messages by recipient and only show notifications when they're filtered to you. There are a lot of options to have it work pretty much any way you want.
Hope this helps!