Yes, don't disable link underlines within the code blocks, let the default be. It's not like there's a competing convention for underlining within code blocks.
It might also be worth having those links opening in new tabs as an option. Right now, at least on iOS, following a link and then going back leaves you at the top of the original page again, not where you were up to before you clicked the link.
In general, it's better for sites to not take away from the user the choice of opening a link in a new tab or not. When I follow a link on my iPhone, when I use the Back button, the page is still scrolled to where it was before, which is my typical experience in mobile Safari.
In general, I agree. But if the link is a surprise because the styling isn't obvious and it might easily be tapped while trying to scroll content on a small touchscreen and it breaks normal back button behaviour, I disagree in this specific instance. All of those things were true in iOS Safari on my iPhone at the time I wrote that comment.