There is a company I love but I think they could improve their social media presence. I sent them a message offering to work for them on a part-time basis. I didn't get it.
I've seen this approach pay off for a few people - Randall Kanna, Daniel Vassallo and Philip Kiely were hired by Gumroad after pitching their services on a part-time basis.
I guess it's normal that you only see the successes and you don't see the rejections.
Any way, I didn't hear anything back and I worded the message in such a way that if that happened I would get the hint and wouldn't hold a grudge.