If I were Google I'd trust links from a site where there was either - a application / peer review process plus 'hub authority' (i.e. trusted by experts), or - moderated consumer rating system plus 'hub authority' (i.e. loved by the public)
But I'm not Google and, as you say, who knows what they think.
>>Will that help my page rank if the links are dofollow?<<<
>>>Will Google penalize me for publishing free open source helpful software on quality sites?<<<
If you create a widget Google want you to use nofollow on any links you build into it back to your own site, so from a ranking point of view the widget is useless (if you nofollow) but worthwhile for any direct traffic it generates. As is my understanding of google right now.
Submitting your software to software reviews sites that are quality and will send traffic should be a no brainer. The goal in mind is not the link first so I think that factor would keep me on the yes side of things.