guess it depends what customer service department you're calling.
where I work right now, emails are generally responded to within 5-15 minutes depending on how busy it is, and a lot of us vastly prefer emails over calls since it gives us something in writing in case the client later tries to recant and poses fewer risks of one party being misunderstood because of an accent, poor cellphone connection, background noise, etc.
and for inter-office stuff, I mostly 100% require something in writing just to make sure that my ass is covered. I got burned pretty bad on that once, where I spoke to someone in-person about something and they later denied that the entire conversation ever took place