Joining to Special Editions of games, while owning a normal edition

Technically, you can (the button won't say that you already own the game)

It is best to ask the giveaway's host if he's okay with you entering for dlc/upgrade.

Tough question.. On one hand, it isn't forbidden (I don't think there is an explicit rule about this), but on the other hand this mean the base game of the pack would be "wasted" if won by someone who already owns it.
That's why I don't enter these kind of giveaway if I own the base game, i'd rather see someone else playing this game for the first time than me winning a DLC.

But, as previously said, asking the creator of the giveaway is a good idea.

I think it's gifters choice to give the game to you or ask for reroll. I once entered the giveaway for fallout new vegas ultimate while already owning new vegas and the gifter asked for reroll. I think it's not fair, but rules are rules.