It depends what you want to achieve
By substituting pixels for ems you have in fact made another fixed width site except that it will expand and contract depending on users settings which is a good thing. However it does not address the issue of screen width and what the site looks like on smaller or larger devices than the one you designed it for.
You should really be designing with min-width and max-width in mind so that the page can grow and contract depending on screen size. Of course that means being careful with how the elements are laid out so that they can ebb and flow with the screen size nicely.
You could set a max-width of say 61em and use margin:auto so that it centers on screen.
Fluid/elastic sites present some design challenges but as long as you don't try to constrain everything into little boxes then you should be ok.