From a biblical perspective (yeah I know, I can hear you all groaning now, haha) - No.
Fallen angels are able to pose as people whom were once living, but are now long dead. When a person "remembers" a past life, they are essentially being given information through a first-person observer: A demonic entity. A third of the angels followed Satan at the fall, and that is a lot of fallen angels.
"And no marvel; for Satan himself is transformed into an angel of light. Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works." - 2nd Corinthians chapter 11, verses 14 and 15.
Since these fallen angels have no need to eat, sleep, or whatever... What else do they have to do with their time except deceive people of the truth? It doesn't even have to be a compelling lie, just anything you want to hear that will lead you away from the truth according to the bible. The truth being (according to the bible), that when we die, we don't come back in a flesh and blood body: No reincarnation.
It doesn't surprise me in the least, that these entities who neither eat or sleep, trick people into believing that they are reincarnated from the lives of people that demons have observed in the past.
"And as it is appointed unto men once to die, but after this the judgment:" - Hebrews chapter 9, verse 27.
It might sound compelling and nice to think that we come back in repetitive cycles, and see other relatives from "past lives", but I for one do not want to come back here at all. Why would I? So I can possibly die a painful death, all over again? No thanks. Once is enough for me, and I look forward to heaven.
Plus, I would dread to think that I have slept with a sibling (or for that matter, another close relative) of a past life, unbeknownst to either of us. I would have to live a celibate life, just to avoid that nonsense... lol.