Yes, it's possible but it'll need some customisations to the interface.
There's a Start Teach and Stop Teach button on the MDI page but it records the commands you input thru MDI. In order to it with point that you jog to you'd have to add a button or two to the screen so it can record the positions and write it to the file.
1) Do you have any experience with editing the screens and macros inside Mach3?
2) Are you using the standard 1024.set screen or something else?
3) Do you want the ability to choose if each teach in point should be moved to with G0 or G1?
4) Do you need to be able to enter a specific filename each time or is OK if the file created has the same name each time which you then simply rename after it's "recorded"?