If I put the same press release, promoting my new site, on 20 of those free press release sites, will Google penalize me for putting out duplicate content?
No of course not, but it's likely some of those will be kicked to supplemental results if they're all duplicate.
Thanks for that. So, I am I getting any benefit from posting it to 20 sites or should i just put it on one?
the release itself is not but if it keeps getting republished and scraped, the duplicates are obviously dup content
You'll be better off publishing slightly different versions of the same article/press release. Varying the content some and the title will help ensure most stay in the index.