Probably not, iOS 9.3 really doesn't add anything to older devices like the iPad 2 or iPhone 4s. For example, Night Shift mode is only available on devices with 64-bit processors. Apple tablets with 64-bit processors include both iPad Pro models, both iPad Air models and the iPad mini 2-4.
iOS 9.3 also adds new Apple Music features to CarPlay, which is an iPhone-only feature, new Health app features and the ability to password protect notes in the Notes app. These new features are nothing to get excited about, and the iPad 2 doesn't support most of them anyway.
Apple has supported the iPad 2 longer than any other device, but it may be time to start considering an upgrade. The iPad Air 2 was recently discounted by Apple to $399 for the 16GB WiFi-only model, and the 9.7-inch iPad Pro is now available for pre-order.
If you do decide to upgrade, make sure to download build 13E236, because the previous build was bricking some iPad 2 models.