Certainly not. The cross came to be a symbol of Christianity as a reference to how Jesus was brutally nailed to a cross and left to die. As this was a common punishment in Roman times, I hardly think that the Romans were making references to Egyptian symbols thousands of years old in their methods of execution. "Goodness and beauty," indeed.

You say "surely it isn't a coincidence" but probably it is. Suggestions for the origin of the nefer hieroglyph include heart and esophagos, of else a lute.

The thing you are dealing with is that a simply cross shape of two bars is a very simple geometric design, so it's no surprise that it might turn up in all sorts of configurations of symbols. This is mere coincidence, unless you can show some kind of relationship. Parallel geometric designs is far from sufficient.

The use of the Christian cross is very clearly rooted in the belief that Jesus died on a Roman cross, a historical basis for the development of that symbol. It does not begin 'abstractly', but on a claim about what happened to Jesus, and then becomes a slightly abstract symbol, but even then it is a symbol for Christianity, not a generalised symbol of 'goodness, beauty'.