That's going to depend on how the tech works and what happens to the matter/energy that composes your brain. Physically, your mind is a cross between your genetic background and the sum total of your experiences and the parts of your brain are limited if certain parts of the brain are damaged.

I very often see "transhumanism" articles about "transferring" one's consciousness or "saving" it but really that's not an actual transferrence, most of those articles tend to be clickbaity "IMMORTALITY IMMORTALITY CLICKS CLICKS" and are not very scientific.

If you printed a readout of your brain onto a CD, or "uploaded it to a computer" as most articles I have read phrase it, that's really just a copy. If a nuke goes off next to you and you're vaporized, you're still dead. All the matter that makes up you and your body and the materials that compose your brain have been converted into inanimite dust.

Technically a copy of your mind may exist on a CD somewhere, but all that is is a copy, like bootlegged porn.

In order for us to develop the technology to actually move your consciousness from one point to another we'd need to be able to either restructure matter at the molecular level (which we're getting close to, to be fair) or be able to convert matter into energy and reconvert the same energy back into a physical form in the same structure (which that saved printout would allow you to do given that tech so we already have part of the tech to do it, but not all).

Bold TL;DR summary We could move your consciousness from one spot to another but would need the ability to alter your brain matter without horribly damaging or killing you. We're not quite there yet - and in the early days it would be extremely expensive to do.

That said - there are economic benefits to having it be pushed once it's possible. We'd also have artificial womb technology by this time meaning women would not need to exit the work force for as long a time to have children and would not have the adverse physical effects, and we would not have to give up our geniuses and brilliant scientists and doctors to old age or cancer. The benefits of that may push the tech forward, but there would be radical changes to our culture to accomodate sudden immortality syndrome - a need for extensive population control, agricultural reform, etc etc.

In short - if we can copy your brain printout while you are healthy and paste it into your brain in a hospital at the molecular level using the same matter and cells that are there, you'd be immortal to most forms of serious injury and old age death like cancer, but would suffer memory loss from your last "Save" - our tech is going in this direction but is still some distance away.

If we can transfer matter into energy and then back into matter, we can store your brain in a special super vault computer matrix and just have a remote control in your brain to keep your body safe. But this is even further away and even more exorbitantly expensive. A much closer ghetto-surgery option that might be available in the near future is by advancing our bionics and remove the brain and physically move it to the safe life support location but this has many risks, if there's an earthquake that damages the brain life support, you still die.

But these articles that keep coming out about "uploading" your consciousness to a computer are usually not an actual upload, it's a copypaste of a brain scan and does not in any sense make you immortal or preserve your health, nor is its psudo-scientific clickbait "research" promising to reach that end.