Yes, as Tim said, a properly made twist splice is a very good connection.
Not directly related to splicing coil wires:
There are special tools made for twisting wires in communications wiring. I have some from my old air traffic control wiring days splicing 104-pair cables. Back then I could look at a wire pair and tell you its number with just a glance at the stripes. The tool was pretty neat - you strip the wires with it, grip the wire ends in the jaw tips, and pull back. A spiral shaft spins the jaws, twisting the wires with the exact right number of twists. Clip the ends and move on to the next pair. Nowadays, it is mostly done with push connectors and auto-splice clips. We would have to heat shrink cover every splice and them pack the whole connection in a sealed housing filled with insulation grease. It was time consuming, but these splices were made to last centuries.
When you just grab two wires and twist by hand, you have a good chance off one wire spiraling around the other. This connection may come loose later on, and is electrically poor as far as current capacity.
The ever popular wire nut is OK, but unless properly used, it makes only a fair connection. Most people twist the wires, clip the end, and then put on the nut ( read above comment as to why that is bad). That is wrong. You place the trimmed straight wire ends side by side and place the nut over them ... then twist evenly and firmly. This will spiral both wires into a proper twist.
The most common home electrical failure is in a wall outlet box in the wire nut junction bundle behind the outlet. The wires can become oxidized over time and start building up heat as well as improperly installed wire nuts letting a wire come loose and arc.
