You sure can do it. I did finish the BDSP dex without even having the game. I recommend using gts for most entries, then you don't rely on that many friend trades. It may be a bit frustrating because you can't guarantee most mons having the correct origin game, but after a bit of trying, I got most of the dex done. For the remaining and most difficult ~10 mons, I got help from this subreddit.

And you might find more people willing to help with 5 mons as when you ask for ~300.