You can probably do it but you won't be able to install some of the drivers.
I successfully installed Server 2016 on an old DL380 G5 just to see if I could. If memory serves, I got most of the drivers installed, including the ILO2 drivers for Server 2012 (available from the G6 product download pages).
Your best bet is to experiment when you have the time available, and when you can't find 2016 specific drivers, try the 2012/2012R2 drivers since those will usually (but not always) work. Don't be afraid to look at Gen8+ server download pages to see if there are Sever 2016 specific drivers that will work for the G5/G6/G7 servers.