Do you need a beefy computer if you're using a capture card to stream PS4 games?

I recently tried streaming some games on my laptop using game capture on OBS, it worked better than I thought but it still had the quality of a nice plate of mashed potatoes and is totally unwatchable. However, I mainly stream directly from my PS4 anyways which has very limited options. I was wondering if the capture card/PS4 can do the heavy lifting for a stream so I could still layer my cam and twitch alerts onto my PS4's screen? or would everything be bottle necked when the video passed from the PS4, through the card and onto my Laptop.

tldr: Can I use a laptop for streaming if I have a PS4 and Capture Card connected to it?