It sure looks like that is the case. I don't know if if that is typical for a carrier or not. I tried it two ways: (a) only WiFi on, and (b) both WiFi and Mobile network on. In the former case, it blocked until I turned the mobile network on, and in the latter case, it delivered immediately.
It appears that when you send a MMS message, something happens so that the "rmnet0" (Mobile network interface in Linux kernel-speak) interface is brought up temporarily - just long enough to transmit the message to the MMSC server - and then brought back down again. (Whether or not the WiFi interface is still routing packets during this time, I don't know).
That must be the case - you can't even find DNS entries for mms.vtext.com (the Verizon MMSC servers) in the public DNS - only when you use a Verizon DNS server from within their own network can you get a successful DNS name-to-IP (A) record lookup.
eu1