You have a couple of things mixed up, so I'll clear those first before giving you an answer:
Streaming is not necessarily bound to the FPS'es you will get while gaming. Most streaming places (Twitch and Youtube) would offer up to 60FPS. This is from Twitch, for example:
Video Requirements
Encoding Profile: Main (preferred) or Baseline
Mode: Strict CBR
Keyframe Interval: 2 seconds
Framerates: 25/30 or 50/60 frames per second
Recommended bitrate range - 3-6 megabits per second
Audio Requirements
Codec: H.264 (x264)
Codec: AAC-LC. Stereo or Mono
Recommended Bitrate (for maximum compatibility) 96kbps
Maximum audio bit rate: 160 kbps (AAC)
Sampling frequency: any (AAC)
So, this means that, even if you have a 144Hz monitor, you won't ever stream past what the streaming service offers you in terms of "transmission quality". This does not mean that you will also be bound to that FPS cap, so you will be able to see your own screen at higher FPS'es than the stream can display.
On the other hand, as a general rule, anything you want to run additional to a game in your PC will take away from the computer. Particularly, and depending on how you configure the stream (I recommend reading tutorials on how to set up OBS - Open Broadcaster Studio and tweak it to optimal stream/gaming balance), streaming takes a tax on the PC resources. Depending on how you configure it, it will take CPU or GPU, but it will consume a lot of RAM, so make sure you have at least 16GB for decent buffering, even with CS-GO.
Particularly, the choice of components you present are not bad for streaming and should do the job quite fine up to 2560×1440 IMO.
I hope this answers your question.
Cheers!
EDIT: Added idea.