I don't have a good cookie sheet available. Can I use a nice piece of tempered glass as a cookie sheet?
I could see two problems. First, glass isn't very thermally conductive, and it has a lot of thermal mass, so it might take quite a while for the glass to heat up, especially if the glass is thick. This means that you might not get the bottom/middles of your cookies cooked properly; if it takes long enough, they might just dry out.
Second, while tempered glass is made to withstand "reasonable" impacts and temperature changes, what you're describing may not be "reasonable", especially if the glass is thin. The corners and edges would heat up much more quickly than the center, setting up serious stresses. Too rapid a change, or too thin a glass, and the whole thing might shatter.
There may be a magic thickness which neither shatters nor slowly dries your cookies. I won't be doing the experiment; let us know if you do.
Yes you can use a tempered glass baking dish if you have no cookie sheet although you won't get as good a result on it as you would a cookie sheet.
Cookie sheets are thin and very conductive, they heat up and cool quickly which is good for baking cookies. When you put them in the oven they quickly get heat to the bottom of the dough and when they come out they cool fast so the cookies solidify and you can get them off intact. A glass dish heats up much more slowly and cools slowly, when you take your dish out of the oven the cookies will still cook on the dish from the residual heat and getting them off is much more challenging due to the fact the cookies are still molten and the lip of the dish makes it much harder to get a spatula at the right angle.
When I did this before I found that the best results came from warming the dish in the oven before putting the cookie dough on, otherwise the first batch came out all wrong. You want it just hot enough that you can barely touch it, usually a couple of minutes in the oven will do. Take your cookies out a bit before you would with a cookie sheet as they will keep cooking on the dish. Let them cool until they start to hold together enough to get them off, then work from the middle out with your spatula to avoid the side of the dish. Get your next batch on right away - if your dish cools too much you will need to re-heat it in the oven. It's more of a process and it takes much longer then using cookie sheets but it will work.
If you can buy cookie sheets then I would recommend you invest in a couple of them to get the best results. If not then use what is available.
As an alternative you could put all your cookie dough into the dish at once and bake cookie brownies instead. It's much easier than baking cookies in it and they taste just as good.