You have to ask the hoster that will offer the dedicated server. I assume: no. Every offer I know does not mention any graphics feature. There are hosters who offer server with graphics accelerator cards for game hosting, but I bet such servers are so expensive to rent that you can buy a whole PC for the fee of a few months.
In general, OBS will work through a rdp session (remote desktop). I remote controlled my PC with rdp, just like you would if you rent a dedicated Windows server. OBS was useable, although I were not able to watch the preview window or videos in general. That required too much bandwith for rdp. That means, you are not really able to compose and manage a stream remotely through rdp. In a LAN environment you have enough bandwith, but not with a narrow DSL line. You said you have low bandwidth at home, so it seems unlikely that you will succeed in remote-controlling OBS through rdp or vnc. Webcam is not possible to redirect, gaming as well not possible on a server, so I assume you don't have anything interesting as source.
If you don't tell in more detail from what sources you want to produce your stream product, I would say trying to use a dedicated server from a hoster will not work.
