No they don't show any promos in Australia on Home and Away's double episode on Thursday after the first half of the double episode.
At the end of the first episode, it goes to an commercial break at about halfway the mark and then the second episode starts. Sometimes it's even hard to tell that the second episode has begun until we see characters that we didn't see in the first half of the double episode.
I am curious to know why in the UK they show Thursdays and Fridays trailers on Wednesday but also show Fridays trailer on Thursday, my point being that if they can do editing for the UK audience on Thursdays episode why can't they just do it for Wednesdays episode.