Starches, whether it is flour, corn etc... require significant heating(as in bring to a boil) to really thicken. So dumping it in won't do that much. It will do a little though. If you must, choose cornstarch, it thickens better and won't leave a pasty taste. Plus it gives a nice "shine" to sauces. To use cornstarch, make a slurry with the starch and water and stir it in.

Cheese will thicken the sauce as well, this might be the best option.

I don't use freeze dried stuff, but I have noticed all my friends who do, they don;t add as much water as the package says. Maybe less water and the aforementioned problem will be a non-issue.