Absolutely not!
First, consider the size of thread. If you do not know what you are looking at when you start crocheting that fine cotton thread, you will have a royal knot. (And manufacturers do not even make thread as thin as was once used!)
Second, think of how you are supposed to crochet yarn: loosely. This is easier on the hands, eyes, et cetera. Lace should be crocheted somewhat tightly—your hook should never squeak, but there should not be any slack thread, either. It is a fine-tuned balance that requires precision of tension. If you crochet lace loosely, your lace is limp and tends to bunch up. If you crochet lace tightly, you wear the finish off of your hook and make your hands hurt from having to force the hook through the fabric. While learning, you will not have the fine control over your tension that you need, because tension control comes with practice.
Third, do you really want to begin with the tiny steel hooks, some of which you can barely see the head on? Do you want to be learning how to use the hook to grab the string with a very small hook?
Speaking of the hooks, though some of the aluminum and steel sizes overlap, use steel hooks for thread. They work much better. You can use steel hooks for yarn, too, but be careful, as it is a little easier to split yarn with them.