IP-telephony and recording of conversations - is it possible without the Internet? Besides GSM-like cloud telephony?

Question

API

Hello.
Tell me, is cloud telephony possible, on a regular push-button dialer, without the Internet? And so that the records of conversations and the whole history - everything was recorded somewhere on the server?
That is, it is quite interesting that the cloud virtual PBX beeline and megaphone, for example, save a conversation record to their cloud, even if the phone does not have Internet.
If you use other IP-telephony - it will fall without the Internet, otherwise there is no way? I understand correctly?
Thank you.

Answer 1

IP telephony works without the Internet. Only works inside the office.
Asterisk can write conversations and call statistics

Answer 2

In any case, a PBX system is needed to manage calls and record.
What to connect to this system - an IP telephony provider or a GSM operator (through a hardware gateway into which SIM cards are connected), or to encrypt the E1 channel - the choice is yours.
The last two options work without the Internet.