Can you get blocked from commenting in your own group?

Is it possible to get blocked from commenting in your own group if you make the same comment in multiple posts with the same text except for tagging different members each time, with a link to a product?

I've noticed that *way* more people like/comment/share the post than actually click the link in the original post, and I think giving them a reminder to click would greatly increase the clicks to the site.

Yes you probably get block for spamming. Use variations of the text and use link shortener to cloak the URL.
Is the offer your own product?