You can do whatever you like with javascript. But do it carefully. :)
There are many way to achieve your goal depending on what you really need and how many time you can spend on hacking ember/handlebars/ember-data packages.
First and easiest variant is to override render method of SimpleHandlebarsView/_HandlebarsBoundView, which displays simple binded values (there are few other views: for @each, with, etc). This is simple sequence: override method, call an old method, check the result of getting value for rendering, console.warn if result === undefined. You can't get template name inside that method, but you can get parent view for rendered value. So, I suggest to turn on LOG_VIEW_LOOKUPS to easily match views with templates.
Example of console logs:
Rendering application with default view <(subclass of Ember.View):ember226> Object {fullName: "view:application"}
Rendering index with default view <(subclass of Ember.View):ember251> Object {fullName: "view:index"}
Rendering <(subclass of Ember.View):ember251> , property is undefined: model.undefined
JSBin with example.
Another way is to override handlebarsGet method from ember-handlebars-ext package: https://github.com/emberjs/ember.js/blob/v1.7.0/packages/ember-handlebars/lib/ext.js#L75.
Third, if you need to catch accessing to undefined properties of Ember.Objects, you can override unknownProperty method for those objects.
If you need to check a rendered data quickly, you can use {{log model}} method in Handlebar's template.
You can get deeper into patching and rewriting core of Ember, of course. But I advise not to rely much on inner structure of libraries. Good luck!