Regardless if you are not actively accessing the internet via Verizon's cellular network?
A call cannot be received while actively accessing the internet via Verizon's cellular network. It is my understanding that with some Verizon smart phones that a message is provided while actively accessing the internet via Verizon's cellular network indicating there is a call and do you want to accept the call. Not sure if the same is available with the Verizon iPhone.
Wi-Fi has nothing to do with Verizon's cellular network.
You can place and receive calls while actively accessing the internet when connected to the internet via an available wi-fi network.
You cannot place and receive calls while actively accessing the internet when connected to the internet via Verizon's cellular network.
You can place and receive calls while actively accessing the internet when connected to the internet via AT&T's 3G network, but not with Verizon's network. When actively accessing the internet when connected to the internet via AT&T's non-3G network when a call is received, the call will go straight to voicemail without a notification that a call was received and do you want to accept.
Okay, i get that. Maybe I'm not getting something though, as I'm not "actively" using the internet, i.e., the phone is sitting on my desk without me touching it... and still, the calls go to voicemail.
You don't have to be touching your iPhone for it to be actively accessing the internet at a given time. If you are accessing an email account that supports push access for received messages or have an email account or accounts set to be automatically checked for new email in the background, if the incoming mail server is checked for new email and new email is being downloaded while connected to the internet via Verizon's cellular network when a call is received, both cannot be done at the same time.
Just one example.
How many calls are you taking about? One or two, or a number of calls?