On page 648 of A New Kind of Science, there's a definition of a "universal" cellular automaton, which can emulate Wolfram's 256 elementary cellular automata. Furthermore, it emulates them in a "cell-by-cell" manner: one cell of the elementary automaton is represented by 20 consecutive cells in this cellular automaton.
Elsewhere, on page 437, there's a definition for a family of reversible 2-color cellular automata. I expect that in a family like this, but with more colors, you can construct a cellular automaton that is "universal" in the exact same sense as the one on page 648: one that can emulate all 256 elementary cellular automata, and which represents them on a "cell-by-cell" level, using consecutive cells to represent one cell.
I feel sure someone has made something like this, but I don't know the cellular automata literature. Could someone point me to it?
There is no precise definition of what "emulating" means in the book of Wolfram, but it looks like intrinsic simulations (like in the notion of intrinsic universality, see this survey on universality in CA). In this case, the answer is NO, because there is no reversible CA that can emulate an irreversible CA.