Of course it is possible. You can add udev rule to run specific program on device connection. Add file /etc/udev/rules.d/99-USB.rules with content:
Code:
ACTION=="add", SUBSYSTEMS=="usb", ENV{DEVNAME}=="/dev/*", ENV{DISPLAY}=":0", ENV{XAUTHORITY}="/home/YOUR_USERNAME/.Xauthority", ENV{DBUS_SESSION_BUS_ADDRESS}="unix:path=/run/user/YOUR_USERID/bus", RUN+="/usr/bin/sudo -u YOUR_USERNAME --preserve-env=DISPLAY,XAUTHORITY,DBUS_SESSION_BUS_ADDRESS /usr/bin/notify-send 'USB device detected on port $env{DEVNAME}'"
Change YOUR_USERNAME to your real username and YOUR_USERID into your real user id (you can get it by command "id"). If you need automatic detection which user account is currently logged in GUI you would need more sophisticated approach.
You can specify more or less matches in rule depending on used devices, for only USB to serial converters add SUBSYSTEM=='tty', look in "man 7 udev" for more info. And for "notify-send" you need to install "libnotify-bin" package. You can for example change icon for message and time to display.