What you're describing is in effect an internal, biological form of gene therapy, an experimental medical treatment that seeks to treat or cure disease by altering the genes slightly to make the person being treated more resistant to the disease in question.
The problem is that we don't really understand what causes aging just yet, but one theory relates to a component of DNA called Telomeres, which appear to shorten with each replication of that DNA, ultimately putting a limit on the number of replications that can occur within an organism. The link also gives a wide range of different aging theories, all of which may assist you with forming your own conclusions regarding your answer.
To me though, the single biggest issue here would be longevity of the 'embryos' within your elf. It is generally believed in scientific circles that women are born with all their possible eggs within them, although there's been some recent debate about this given the discovery of stem cells within the ovaries, but in any event, women are born with a LOT of eggs inside them. The problem is, they start to die off immediately and continue doing so. By the time a woman reaches menopause, the few eggs remaining to her are more or less unviable. IVF has cheated this and allowed older women to have children by re-implanting eggs that have been harvested previously and fertilised, but generally speaking, a woman's eggs are not going to last 100 years, let alone 600, and your elf will suffer the same problem.
At the end of the day, especially in a warm blooded species, all parts of the body are going to be subject to entropy to a greater or lesser degree and given the sophistication and delicacy of DNA, the odds of keeping renewal gene pods inside a warm body for centuries, not subject to the normal renewal processes of the body and not subject to normal biological breakdown are remote.
In addition to this, there are two other factors that you really need to consider. Current natural DNA replication methods have many checks and balances built in already to stop errors (read as mutations) being introduced. These are not perfect, but given the amount of work they do over the course of a human lifetime, they're VERY reliable. Your design effectively hacks that process once every 60 years or so and feeds it a new template, which introduces all sorts of risk vectors. For one thing, diseases now have a new mechanism that they can exploit to get DNA to replicate of a different template completely, potentially introducing a runaway cancer scenario that effectively uses the body of the elf as raw material for the production of cancer cells on a massive scale.
Additionally, memories are even trickier. The problem is that we really don't know how they're laid down or stored in the brain, despite a lot of research in this area. It's possible that memories are just encoded electrical circuits in the brain, in which case you really don't want 'renewal' in that part of your body as it could potentially cause massive disruption. If memories are somehow encoded into the cells or into the pattern of connection between brain cells, renewal could be even more disruptive to memory, personality, etc.
In short, you're trying to bypass the natural aging process by internally storing cells that somehow bypass the aging process. Is it possible? Yes. But, it's highly unlikely and would involve organic 'storage' mechanisms that have yet to evolve despite them having a material benefit to procreation before longevity.
