Posting new content to blog.corporate.com is still better than publishing nothing at all. For SEO it won't help www.corporate.com as much as www.corporate.com/blog/ would help, but SEO is not the #1 goal of every content program.
You can still get tons of value from driving qualified traffic to blog.corporate.com using tactics like Facebook Ads and other paid social media, and that blog can still rank in search results and eventually drive prospects back to www.corporate.com. As Patrick mentioned, creating links in blog posts that point back to key pages on www.corporate.com will help on the SEO consideration.
So to answer your questions:
1 - Will it help boost ranking of example.com if we share frequent content on our blog https://blog.example.com/? How much impact it has?
Yes, but good internal linking will be help. It has less impact than if you were to get that content onto www.example.com/blog/.
2- Everybody says content is the king, Ok fine, but when you are not allowed to share it on the main corporate site, then where to share it? Blog and social media sites? please help.
Subdomain is next best option if a subfolder on the main site is not an option. So, post content on blog.corporate.com - and then share that link on social media.
3- We are in a business where clients do not bother to go on sites and read, so in this scenario is it correct to say that you hav to create the content for search engine consumption even when your clients dont need it/or have not in the habit of reading it?
In most 'boring' industries there are still decent ways to get users on to the website reading your content, you just have to be more creative. Here's a few posts with ideas and examples:
