Running a server completely headless is fine as long as the server boots and remote access is available (via ssh, rdp, vnc or similar). I have a HP mediasmart EX490 server which has no VGA output (though it is possible to get a VGA/PS2 connection with a debug cable). These are some tips for running the EX490 completely headless with Ubuntu.
HP EX490/EX495 MediaSmart servers were at one time very popular option for a home server. These 4-bay home servers came with Microsoft Windows Home Server V1 as the operating system. It was a very small (even smaller than the newer Gen8 ProLiant Microserver) yet feature rich home server. I bought mine in 2011. This post is about some history of the upgrade path of my EX490 and a recent update to a 6TB GPT boot disk.