I don't know what a 'streamer' is but what Bob said still stands the best method is to add the appropriate fx after recording. I know I would hate to 'stream' for a couple of hours only to find that the myriad of fx I had permanently recorded didn't actually sound any good in the cold light of day but each to their own.
I would suggest that the best way to make a microphone sound better is to get hold of a good quality microphone and preferably one which suits both the subject's voice and the subject matter and use it in a suitably treated room - anything else is just chasing your tale.
"I have tried soundflower although once I try streaming with obs no sound goes through" - hopefully Bob knows what that actually means and can throw some light on it for you.
I think what the OP wants to do is use Audition, in effect, as an outboard processor while streaming audio live to the net rather than simply recording it. Please tell me if I have this wrong, Thomase?
From what I can see, he's trying to route the input (with effects) to the web rather than just to a headphone output--at least that's what I think they're doing with Virtual Audio Cable in the video he links to.
This obviously isn't what most audio software is made for--even in live use, normally you take an output of the computer to a PA system or whatever rather than streaming it.
Soundflower is suggested as one of the Mac-compatible equivalents to VAC. From what I can read on line, it sounds like it SHOULD be able to do the job. However, if it's anything like VAC, the set up is a pain and takes a lot of fiddling to get things going where you want...so it might be worth playing some more. Also, I did some Googling and came up with another app called "Sound Siphon" which specifically says it can be used for streaming. It might be worth a try. Sound Siphon Alternatives and Similar Software - AlternativeTo.net
However, I'd repeat that this isn't really what Audition is made for and, at $20 a month for a subscription, you could fairly quickly get the budget for a better mic...probably some kind of dynamic you can work close to. At the economy end, I might suggest a Sennheiser e835 which is flattering on many voices. A bit of soft stuff around the room and working in close for proximity effect and it might sound quite good. Couple this with a cheap mixer like a Behringer Xenyx Q series and you'll get basic EQ and simple compression (with a USB out) and you'd probably get what you want in a package actually designed to work that way (and sorry Adobe if I talk you out of a sale!).