As the link you provided explains, statlessness and refugee status are not mutually exclusive. Anyway, after a bit off googlefu I dug up this:

UNHCR‘s Handbook on Procedures and Criteria for determining Refugee Status provides in paragraph 184: "If the head of a family meets the criteria of the definition, [for refugee status] his dependants are normally granted refugee status according to the principle of family unity."

In effect, refugee families everywhere retain their status as refugees until they fall within the terms of a cessation clause or are able to avail themselves of one of three durable solutions already mentioned -- voluntary repatriation, local integration or resettlement in a third country.

Also, Chapter 5 of the UNHCR publication, Procedural Standards for Refugee Status Determination under UNHCR’s Mandate is very clear that in accordance with the refugee’s right to family unity, refugee status is transferred through the generations. According to Chapter 5.1.2 "the categories of persons who should be considered to be eligible for derivative status under the right to family unity include:" "all unmarried children of the Principal Applicant who are under 18 years."

Chapter 5.1.1 makes it clear that this status is retained after the age of 18. It states "individuals who obtain derivative refugee status enjoy the same rights and entitlements as other recognised refugees and should retain this status notwithstanding the subsequent dissolution of the family through separation, divorce, death, or the fact that the child reaches the age of majority."

In addition, UNHCR typically cites a Palestinian refugee population number in their State of the World‘s Refugees reports: see as an example this document. This makes clear that the practice of registering descendants of refugees is not disputed.