Renovation will cause more dust for sure. However, if you can close off the upstairs and not use the central heat/ac you will be o.k.

Floors go in last. Gravity works and boots have to walk on something. That means any flooring changes should be done LAST. Use/destroy the current flooring and then once everything is all done, you rip it out and install your new carpet. You will be VERY happy you did.

Even if the works are happening downstairs and not upstairs?

It is your call. But ask yourself this:

"Can I accept the results if something goes wrong? Especially if I was warned about it before I let it happen?"

Upstairs will be fine....We did a tear out a wall, make a new room, re-do an old one.....and the existing carpet and rugs were fine. I vacuumed extensivly every day after the workmen left.....and as I was tearing my hair out, a friend who had recently done something similar said "You think it well never be clean again....but it will be".
Dust doesn't ruin carpet....ground in grit may....but not dust. Do you have a vacuum? and perhaps drop cloths? Cover the upholstered stuff and maybe your beds and vacuum the rest every day.
And change your vacuum bags often!