Should I be able to make a tarte tatin in a glass dish?

Technically you should be able to make almost anything you'd be able to make in a metal dish, in a glass dish, but if the preparation calls for one then you can't simply substitute the other willy-nilly. It will likely require a good deal of fine-tuning.

Glass is an insulator. It absorbs heat. That's why solar panels are glass and why having a window in your home is not like having a gaping hole in your wall. As a consequence of this, (a) it will take a longer time for the dish itself to come up to oven temperature, (b) it will cook much more consistently and evenly, even if you have an oven that turns the element on and off to maintain temperature, and (c) it will continue cooking the food after you remove it from the oven, unless you remove the food from the baking dish immediately.

What this means is that you generally have to extend the cooking time by at least 5-10 minutes (more if you are baking at high temperatures) when substituting glass bakeware for metal, to let the dish "pre-heat." Except if you're going to let the food cool inside the baking pan, in which case you might actually need to decrease the overall time to prevent burning afterward. It's hard to be precise because it depends on what you're cooking, how long you're cooking it and at what temperature.

To be honest, I probably would not use a glass dish for any recipe requiring caramelizing because caramelizing relies entirely on finely-controlled conduction; ovens are less sensitive than a stove top but nevertheless, a few minutes too long and it's burnt, a few minutes too short and it's still solid. Better to choose a material that's highly conductive for that, i.e. metal. Glass is best when you need slower, more even cooking, like casseroles.