[manu666]

@ manu 666, yes exact , but now you can have sufficient power in your NAS to do a HTPC without bying another box , for example a raspbery pi or other , and a very good quality , even better than HTPC of 2 years ago .

I understand your point of view but that's not mine. And you are probably right about the power of nowadays NAS. Bur a NAS next to my TV, in my living room is everything but WAF :-)
And I have several TV at home, so I need several clients (or front end) to display movies on TV screen, and RasPi is very cheap.

so why paid more to have less quality ?

and why by a box to do one thing ? you dont by a NAS for samba , another for ssh , another to serve webpage , another for VPN , etc .... so that it is able to do more and more , everything depends on its abilities .

according to me a NAS have to serve files , what is the difference with XBMC ? it serves files too and displays them if asked .

Giving access to files and decoding video files are two different things. All the more XBMC is not only decoding video files, it also comes with a GUI who needs some ressources (depending of course of the skin your using). The primary task of a NAS is to manage several hard drives with redundancy and quality control of data. For that you need a good raid controller. So I prefer a machine with a good raid controller, than a machine with a average raid one and a graphic card (or at least decoder chip). More over if you want one day to invest in 4k screen, you probably have to change your NAS used as HTPC instead of changing only your frontend.

Besides a multimedia server comes automatically with synology, and there's another minimum (plex) in deposits

Yes but in the case you want, as I am, a xbmc on your nas, to scrap your new files (so your XBMC "client" don't have to do it when it starts) and have access to your library on-line, as it also comes with DNLA fonctions you don't have to run the synology multimedia server and then save some ressources on your Nas.

So to come back on your primary question, I have really no clue. Check with docker image with a full kodi (not a headless one, as it doesn't come with a GUI and video decoding functionalities).
What is your Synology model ? On Synology web site I don't find any NAS with HDMI output.