Does Jonas from the book The Giver appear in this book Gathering Blue, which is a sequel to The Giver?

The answer is both yes and no. Gathering Blue is set in a village that is very dissimilar to the community which Jonas leaves at the end of The Giver. Kira, the main character in Gathering Blue, never leaves the village in the course of the narrative, and there seems to be no connection between the two books at all. 

However, at the end of Gathering Blue, Kira's friend Matt sets out in...

The answer is both yes and no. Gathering Blue is set in a village that is very dissimilar to the community which Jonas leaves at the end of The Giver. Kira, the main character in Gathering Blue, never leaves the village in the course of the narrative, and there seems to be no connection between the two books at all. 

However, at the end of Gathering Blue, Kira's friend Matt sets out in search of the blue, that is, a plant or some other substance from which blue dye can be made. When he comes back, having accomplished his goal, he tells Kira that he has met a boy whom he thinks Kira would like. One of the reasons he thinks that is because that boy has blue eyes. This gives readers a clue that Matt has met Jonas, whose blue eyes are an important detail in The Giver, even though they are described there not as blue, but "pale." So while Jonas is never mentioned by name, one could say that he does appear, however fleetingly, in Gathering Blue.

The fact that Jonas has survived the journey from his community is confirmed in the book The Messenger, and in the final book of the quartet, The Son, Kira and Jonas are a married couple.