I would even say you could use VNC (I would use it via an SSH tunnel or VPN don't just expose VNC port to the world it's VERY unsafe if you do not (see port forwarding over ssh tunnel for easiest way to secure such a connection).
Anywho this would allow you to view your progress, and then you could even run a couple extra commands (if comfortable with the terminal and command line you could even just use SSH server alone and when connect you could always bring up a background job (I recommend JuiceSSH).
As for exactly what you are asking it would seem to me if you say wrote a quick shell script that calls your command and when done also edits a simple text file. Then anything that can connect and check for text file contents (say write a shell script for your android (see: https://play.google.com/store/apps/details?id=os.tools.scriptmanager&hl=en)). You could say setup a samba share for the directory where you store the text file then setup a quick script to wget the text file and print whatever on your screen.
All in all I would say from the sounds of a developer angle you may prefer to setup openssh server, then install x11vnc, setup a script (I use xUbuntu (XFCE4 and not unity) and a simple upstart script to start VNC on system start and anytime I issue sudo service vnc restart. Once you have the SSH and VNC server command running you can then use any ssh client (again can't say enough about Juice SSH it does port forwarding in a snap). Once setup, for me I tap on icon on my home screen to connect the port (auto passes my user/cert and all), and then I open Jump Desktop and tap the entry for my server and it auto passes my VNC password so I only have 2 taps and I am in with full security. If needed NoIP.me still does free Dynamic DNS so you can get an account and then use an address that never changes (ie. user.noip.me) instead of having to memorize your home routers WAN IP and remember to check every time it changes.
Sorry if this sounds a little long winded. I am unaware of your tech expertise level, and I wanted to not only try to specifically answer your question as posed, but also share my personal solution as this would allow you access from anywhere (unless using a Wi-Fi that filters your SSH server port or if you have no data connection), AND not only see if the work is done, BUT you can also interact with your desktop as if you were sitting in front of it and fix any maybe small compile issues or make that adjustment before you forget type of stuff. I use Jump Desktop a TON and it is fully capable (even handles M$ Remote Desktop as well).
Please let me know if you need me to explain anything, or adjust it if you are using Windows (I use xUbuntu 14.04 currently which is FREE, and desktop mimics Windows somewhat closely so if you are a Windows Dev and would like to try out Linux I recommend it HIGHLY)).
Anywho, hope this info helps.