wp_list_bookmarks does not create any sort of "current" class like the other pages do, because it is designed primarily to link to external sites instead of internal ones.
So yes, you can use it in the way you are thinking, but it's not the best way to do it, and you can't get "current" links out of it at all.
On the other hand, while wp_list_pages does make you use the "Title" as the link name, maybe you should make the Page Title into "Welcome" and then use a Page Template that does not show that Title. In other words, make a "No Title" Page Template, use it for your Pages, and then as the first thing in the content of the page, put the real title you want, like
<h3>Welcome to our site</h3>.