Is it possible to write to serial terminal program via JTAG interface?
Most likely yes, however it may be tricky.

If the micro does not have programmatic access to the jtag pins, you may have to use debugger functionality such as breakpoints and reading/writing volatile variables to accomplish mailboxing data interchange.

Ugly to implement, potentially problematic if you have realtime tasks, but the beauty is if you make it work it's all software so you can abstract the ugliness into a library on each end.