Yes! If you don't have an iOS or Android device, you can use a friend or family member's device to upgrade your Gear and then track your achievements with the AvengersNet App.
Follow the directions in How do I register my Gear with the AvengersNet App? and How do I upgrade my Gear using the AvengersNet App?
Make sure your friend or family member logs out of their Disney account in the app first. Then, when prompted to log into an account, enter your Disney account username/email address and password, or register for an account if you don't have one. Your Gear will be registered to the app under your Disney account, and you can download and install the upgrade, then track your achievements!
Remember to log out of your account when you're done.