I've used NE570's in a commercial project as compressor limiters , and they worked well - but it wasn't a hifi or professional audio product.
If you want to do this digitally , you can't use the a/d of an arduino as the main audio sampling unless you're happy with poor performance - it's not quick or accurate enough. And you's need an external d/a.
But as a sidechain controller driving a decent VCA - quite possibly . You need the abolute audio amplitude every 100us and drive a d/a at about this rate too.....
I don't say it couldn't be done, but you can can source marvellous digital audio chips incorporating a/d's , d/a's and a serious DSP from many suppliers now... if you want to do this digitally I suggest you go that way.
regards
Allan
edit - most broadcast radio is compressed anyway because a major listener audience is in a car with high background noise. I worked in pro audio for a while and know the tricks.
In the UK the BBC's DAB system uses MP2 compression which is ghastly for qualilty, and even their FM broadcasts are 'processed' - apart from radio 3 ( god bless 'em) the classical channel.
The government want to shut down FM broadcasting and sell off the frequencies to commercial uses . I seriously hope they don't!
FM is better than DAB in quality .
Until the days of CD's a live broadcast of a concert on Radio 3 was the best quality you could get anywhere - both to listen to and (if recorded) on a good reel-reel tape machine . I had a REVOX.