no

The ONLY way that superstitious rituals (Otherwise known as "magick" ) work is IF there is a scientific reason behind it.
I consider myself to be a witch, but I base my practice on scientific phenomenon. I consider magick to be undiscovered science.
I don't put my faith in deities. I consider the deities to be ancient mythology that came about from the entire earth observing the astronomy of the constellations centuries upon centuries ago and inventing stories about the star patterns to explain them to their children.
Each culture has their own similar story since everyone was looking at the same thing. Eventually, however, these began to be taken literally, and by mans competitive nature the different cultures began arguing over which one was correct.
Mix in philosophy with that, and "religion" was born.
I study religion for its philosophy, and for its historical value.
Religion has no bearing on my practice. Much of witchcraft has to do with tapping into the frequencies of light and sound, (That can be proven to exist) and the different kinds of energy waves and using them to create causes and effect.
Gatovicolo mentioned that waving your hands in the air disturbs the air a little, this will cause a ripple effect, and a LOT rides on energy waves.
Some of it has to do with psychology.
Benthoven has mentioned the "placebo effect", and that can certainly also play a part.
Much of the rest of it deals with herbs, and potions, and natural healing which all of have its basis in science...
So yes they can, but it is based upon scientific phenomenon, and the right conditions have to be set up in order to cause it to happen.
I won't happen through simple "Hocus-Pocus".
(See my reply on "Do Prayers work" for more info about this)

Beliefs are powerful things, and while they may not be tied to "reality," they strongly affect how we function in certain situations. It's called the "placebo effect."

If you're lucky, yes.

Waving your hands in the air disturbs the air a little.

When we swapped out a PDU in our data center years ago (power distribution unit), we had to shut down every server... it was hundreds upon hundreds of systems and routers that managed huge clients like Starbucks, BMO, various financial institutions... Someone said they sacrificed a turkey to the digital gods. It worked. All systems came back up.

Mind you, it was thanksgiving weekend...

Only in the sense that it may incentivize a person to a greater extent to achieve the intended task or purpose.

Well...I used to be heavily into magic and casting spells, but I came to reality and to understand that most of the stuff that I was casting spells for were already things that would have happened on their own. No spell has ever brought back the leg of an amputee, let alone prayer from a God has never brought back an arm or leg on an amputee. Sorry lol... you said besides magic, but that’s my two cents.

The only way that they could have any effect is to give the believer the confidence to pursue something he or she might not normally undertake.