An interesting question that has more to do with art than religion!
The answer is that it really depends on the artist who made the crucifix. Take a look at a number of different crucifixes…
Some have Jesus with his head bowed depicting his death. The artist wants us to concentrate on a Jesus who died for us. Another might show Jesus kind of pumped up and looking refreshed. This artist wants to show that the cross cannot hold Jesus back from defeating death. A third might show a twisted agonizing face of Jesus which allows the viewer to concentrate on a God who suffers for his people.
So yes, there is some symbolism there but it varies with each artist’s depiction of what they are asking us to contemplate with their work.