No, you cannot connect one cell phone directly with another. Cell phones contain cell modems, which are controlled using "AT" commands, patterned after (but greatly extending) the AT commands developed in the original Hayes modems thirty years ago.
There is a core set of AT commands that are common across all cell modems; these generally have a prefix of "AT+". Then there are a number of proprietary AT commands developed by each cell modem manufacturer, they have prefixes like "AT$" or "AT%" etc where the third character is unique to the manufacturer.
I have worked with cell modems from four different manufacturers. The documentation for these commands typically runs over 500 pages long.
These are all designed to work only with a cell tower. There is a command to get the signal strength (AT+CSQ), which is used to update the bars on the screen. There are commands to check whether the cell modem has registered on the network (connected to a cell tower). Another command to get the list of carriers supported by the cell tower.
For voice calls there ia a command to dial a call (ADT, just like the dial up modems from the past), and another command (or rather set up of commands) to set up a data call via GPRS and request a TCP/IP connection as you found out. When a call answers, or a connection is made to the Internet, the response is CONNECT. The modem then goes into a data wheere data can be sent or received. To get back to control model, the familiar +++ sequence (patented by Hayes) is used.
If these were to work for point-to-point communication with another cell phone, that other cell phone would have to have most of the capability of a cell tower. But there is no provision for that. There are no commands in any cell modem AT set which allow a cell phone to behave that way.