Yes, that is how TCP networking works. If there is no acknowledgement then there is no data to send. Even still before it can send it needs to do DNS resolution to find out what IP address to send to and if DNS doesn't resolve because there is no Internet then nothing gets sent.
What you could do is set up your own internal APRS server, no need to sniff traffic then. A Meteobridge can send to that APRS server internally. No internet required because address resolution is internal network and data is being sent inside the network only. Or you could do the same thing with an ObserverIP that is running older firmware and then you can set up WeeWx to receive Weather Underground data internally, then you can sniff that. Look up Network Redirection and setting up WeeWx with the Interceptor driver.
And I'm sure there are other possibilities, like sending to an SQL or FTP server, then picking up the data there instead of needing to sniff it. The thing is to think to keep it internally. But regardless what option you go with you are going to need the ObserverIP. Unless you can do DNS poisoning to do your redirection and then capture the traffic being sent to WeeWx. Weather Display might be an option too. I see lots of possibilities.