As long as it really believes itself to be me, and does a sufficiently good job of using those thought patterns, I don't see the difference. Ultimately, any distinction will be the machine's to draw.
The question is, do you merely want a version of you to continue to exist hundreds of years into the future, or do you want to live hundreds of years longer yourself (and experience those hundreds of years yourself)? If it's the former, then this is an excellent idea. If it's the latter, it's useless. Robot You will keep chugging along, but Meat You is still going to grow old, die, and end up in the ground, where you will feel and experience nothing.