Our testing and shown that it works in IE11 and above. Both Safari and Chrome support custom elements natively, so no polyfill is required. Additionally, Edge has it under construction, and Firefox has custom elements behind a flag. For Edge, IE and Firefox the polyfills are downloaded on demand, rather than every browser always downloading every polyfill.
You could still include jQuery in your app if you wanted to. However, the Ionic framework itself does not run on top of that extra layer, especially when native javascript and hardware accelerated CSS transitions will be faster.
And if you're already familiar with Angular you'll see that Ionic gives you a big step forward in your development, and you still have all the power your looking for in writing your own from scratch.