Obviously religion offers hope or order through the promise or threat of an after life, etc.. As far as I can tell there's no scientific evidence for immortality, if only because it would be difficult to verify through experiment.
Does that, or anything else, mean it's outside the scope of philosophy? And if so does that suggest disbelief?
Your question seems to hinge on a controversial and disputed premise, that something for which there is no scientific evidence and/or no empirical verifiability is not a fit subject for philosophy. While there are certainly philosophers in sympathy with that premise, there are also those who would contend that it is precisely those subjects which are outside the realm of science that are philosophical in nature.
Historically, immortality has been a major topic of interest for philosophers such as Plato, the Buddha and Bishop Berkeley. As a topic, it would be strongly associated with idealism. The exclusion of topics such as this is the defining characteristic of what are known as verificationist philosophies, of which logical positivism is the best known.
It would be possible to argue, on the one hand that the subject of immortality is properly a matter of religious faith, and therefore that philosophy should stay out of it, or on the other, that it is scientifically unverifiable, and thus no proper subject for philosophy, but either claim is best classified as a disputed minority viewpoint within the wider scope of the field over the course of time.
I would say that 'immortality' is not outside the scope of philosophy. Think about the greeks, Pitagora taught and talked about past lives and he talked about himself that he had 9 past lives. Platon, Aristotel, the Orphic poems, then Marcus Aurelius. Everyone in a different manner taught and talked about an existence beyound the physical one. On the other hand philosophy is the "love of wisdom". But this is an 'immortality' in a "religious" way, which way, i think, is not understood correctly, religions talk about us as spirits that come to this world in a body of flesh. See Hermes Trismegistus idea from Corpus Hermeticum, he says that when we die our body decompose itself in the primary elements and the soul goes back to his righteous place in "heavens". The idea is that we as souls/spirits (there is an amazing difference between these two, you can find it in alchemy, religion, occultism, etc) live in an "etheric" world and descend here - on earth - (see Plotin discourse/dialog 'about One and Unity' to understand the descending and ascending process) in a body to live as a human being. So immortality as the eternal life of a soul is taught in philosophy or at least mentioned.
On the other hand, if you ask about the 'immortality' of our body from 'now' and about our 'now' self and thoughts, consciousness and all the characteristics that define us, i think it is the scope of philosophy too because 'immortality' may mean a healthy mind and body like in 'Mens sana in corpore sano'.
Anyway, 'immortality' is not outside the scope of philosophy because it fascinates us and philosophy is built on the things that fascinate us.
I don't think that any concept is outside the scope of philosophy, so is the immortality. You can see the debates (ex:Descartes) about the duality of human as body&soul where body is taken as mortal and soul is immortal. Moreover, religion is one of the main scope of philosophy as there is branch as religion of philosophy.
