I think its not good to reply with a question so I will first give you an answer: Yes
Now to the questions, why havent you just tried it? (OBS is free)
Why and what games do you want to stream in 1080p?
Are you aware that users might not be able to watch 1080p succesfully?
Are you aware that Twitch.tv for example has big problems to deliver streams with a bitrate higher than 2-3 mb/s?
Are you aware that 1080p might need more than 2-3 mb/s to look good?
Have you thought about doing a 720p stream until you get partnered with twitch and have the option of transcoding for your viewers?
I could probably ask more questions, but these seem to be the main ones you should answer for yourself.
