My son put one layer of mud on the drywall joints without placing tape. Can I still place the drywall tape after the mud has dried?
It depends how thick the mud is.
If it is not so thick that it significantly raises the level, you can sand it lightly, spread a skim coat of new mud, imbed the tape and proceed to finish coats.
If it is a thick, knobby layer, either on the flat or in a corner, you run the risk of a bulging joint if you don't bring it down.
Drywall tape dries with the drywall compound (mud). They bound together while drying/setting.
If you put tape on top of dried mud, you will likely get nothing but bubbles in the tape from ceiling to floor. Bubbles in the tape are air trapped between the tape and underlying mud, and must be cut out and either re-mudded (small bubbles) or re-taped and re-mudded (large bubbles) otherwise the finished wall will not be smooth.
You must sand down the drywall compound so it is below the level of the drywall (if it is in a tapered joint: for corners/butt joints, just sand down almost to the paper), apply more compound, and tape immediately while wet.
Another option is to use mesh tape on top of the dried drywall compound: it can be used on top of dried mud or just plain paper (the room I am in right now has this tape directly on the drywall for its corner joints and has no issues).