"nok" can also mean "probably"/"very likely".
The closest to the original sentence would be "Den/det vil nok gå væk" - "It will probably/hopefully go away."
It definitely is a word. Though widely disregarded for whatever reason. I like it much.
Can this also be translated as something like 'that'll do'?
Maybe? I wouldn't say so. "Det skal nok gå" is something you say to reassure yourself or someone else that something will work out or function properly. It might be dangerous or prone to failure, but we have confidence.