Q: Are these mods Wi-Fi safe?
A: Mostly. Music and stages are all currently Wi-Fi Safe. Most characters are too, EXCEPT for vertex-edited characters (Ninten, Awakening Roy). Basically, if the only change was color, the character will work, but if the shape/model/size of the character is modified, it will de-sync in an online match.
Vertex edited characters work fine online, not sure where you got this information from. You're thinking of model swaps (ex. Elec Man over Mega Man).