Duct tape + spackle to fix hole under window ledge?
Nope. Use proper drywall tape of either the paper or fiberglass varieties. Both are cheap and won't leave you with a gooey, hollow, fragile mess. I also recommend proper joint compound. Spackle is very light and soft and not suitable for filling large depressions. If you're dealing with concrete or regular moisture, consider a setting-type compound for toughness. (It comes as a dry powder and requires water.)


Prefill the hole with joint compound using a small taping knife and allow it to dry completely. Deep fills can take a day or more to stop shrinking and look completely white. A fan helps.
Skim again to wet the entire area with compound. 
Overlay a patch of tape and press it in lightly with the knife.
Either now or after the skim coat dries, skim again to overcoat the tape. Let this dry and repeat as necessary, seeking to apply the thinnest and smoothest coat that seems to do the job. There's very little sanding with a good taping job.
Sand, prime/seal, paint. Be proud that you aren't a hack doing pretend repairs.