You can! You do have to import your entries along with the comments, though, or else there's nothing to stick them on. :) 

Imported comments are displayed as coming from "so-and-so.livejournal.com" and, thanks to the magic of OpenID, as long as you still have access to the LJ account you were logged into when you originally made the comment on LJ, you can log into DW using that OpenID account and still have the same level of control (edit, delete, etc) as you had for the LJ version. 

Or, you can claim your OpenID with your DW account, and then all the comments you've left in other people's journals with that LJ account will update to display as your DW account instead. For instance, look at the comments to this post from 2008, which was originally made on LJ, and was the first time that we talked about DW in public. I imported the entry, and all its comments, from LJ; the first comment thread, now appearing to be from me and zorkian (which is mark's personal account like synecdochic is my personal account), originally displayed like how many of the others still do. (As xb95.livejournal.com and synecdochic.livejournal.com, respectively.) Then I claimed my synecdochic.livejournal.com OpenID URL with synecdochic, and he claimed his xb95.livejournal.com OpenID URL with zorkian, and now anywhere on the site that somebody has imported a comment that I made while logged into LJ as synecdochic, it shows as synecdochic instead!

(It's even smart enough that if you have the same icon keywords on DW as you did on LJ, after you claim your OpenID, all the comments will even display the proper icon.)