Forget the spackling.
Fiber joint tape should never be used in a corner - use Paper Joint Tape instead. It has a seam down the middle, so you can fold it into the corner.
Scrape out the old joint tape, removing any loose compound along the way. Ensure both surfaces are securely attached, to their framing members. Sand any high spots if needed and apply paper joint tape in it's place.
You can use an Inside Corner Trowel to aid in making a smoother joint, while having fewer steps between coating and drying.
If it is a long run, you don't have to do it all in one shot either.
90 minute Lightweight Setting-Type, works great for repairs like this, due to a stronger joint, and quicker turn around while working. You just mix up what you need, and as long as you keep the remaining unmixed powder dry, you can store it for quite a long time.
Asking the basic questions is what gets us started.... not silly at all.
If they are as simple as nail holes from picture hanging and the like, and there are only a few of them, use spackle. It comes in small quantities, pints for example, so much will not go to waste. It is intended for only small holes.
If there are a lot of repairs, you may want to go with joint compound, it is pretty much the same as spackle, it is easy to sand, water based for easy clean up, but you will get a bunch more for the about the same money. It is intended for larger repairs, or new drywall install, can be built up, but it does shrink a bit, not so that it will fall out. If the shrinkage is noticeable, add another coat, no biggie.
Plaster is way overkill for this type of repair, it requires a skill to use. I have tried to use it before years ago, and it set up as soon as it touched the wall, quite surprising. I now know were it is to be used nowadays, and nail repair is not one of them.
Best Answer
Only the lightest of curtains should be hung with hollow-wall anchors in the first place, even if you use togglers (anchors with mechanically-deployed wings). Screw-in or expanding drive-in anchors are almost guaranteed to fail after a short time, and heavy or frequently manipulated curtains should be mounted into framing.
To your question, if you fill the hole well with setting-type joint compound, which is much harder and stronger than "spackle" (a rather vague term leaving much room for confusion), and then you carefully drill for a toggle anchor, you'll probably be ok.