On the schematic diagrams for my crossovers, yes, this is true. They are simple enough that I can draw a schematic with no wires crossing. But reading schematics is a little like reading handwriting. There are some standard symbols, but there is a little room for "flair." To tell the truth, electronics schematics are probably a little more standarized than handwriting, but the same idea applies - Some do 'em a little differently than others.For example, some schematics show every connection with an obvious dot. The lines don't just cross - There is a black dot that sort of highlights the connection. And in some schematics, you'll see a curved line where lines cross that indicates no connection is made. It sort of looks like the wire "jumps" over the other wire, and that, in fact, is exactly what this symbol is meant to show.
I use both of these techniques on schematics of any complexity. If a connection is made, the node is exaggerated with the dot. And if two lines cross that aren't connected, I use the curved "jump over" section. But the crossovers are so simple that none of this is needed. So in this case, a connection is shown by two lines meeting, and you could literally wire the circuit exactly as the lines show and expect the circuit to work. In a sense, the schematic also forms a circuit layout and you could etch conductors having this pattern on a single-sided board and it would work perfectly.
The "bumpy line" is the inductor symbol. The symbol having two parallel lines that don't touch is the capacitor symbol. And the wavy line that is peaked like little triangles is the resistor symbol. I draw the voice-coil of electrodynamic drivers as inductors with a little horn looking thing to represent the diaphragm. And I draw piezoelectric drivers as capacitors with the same diaphragm horn shaped thing.