Yes, yes, yes.
Email is still a great place to build a relationship with your customers. You have to be smart about the content, and the segmenting of your customer lists, but I've seen great results.
Yes it does. Anyone that says it doesn't is just targeting the wrong people or is spamming. Some time ago I worked for a company where we created a community for our most loyal customers and were able to achieve a 10% conversion rate with every email.
People have been asking if email marketing works for nearly twenty years. The answer now is the same as then — yes.
Most of the time when I see email marketing failing, it's because they're spamming.