I'm still thinking. :-) And here's my thoughts:
As Superman of Earth-A only appears in one JLA story -- and even that one performs a self-retcon at the end so it never happened -- the real question at issue is not "shall we include Superman of Earth-A" but rather "Shall we revise the list of canon sources to include the Justice League of America?"
In considering this question, and in view of Super-Monkey's report that All-Star Comics was among Fleischer's canon sources, I decided that inclusion of any Justice Society adventures in TGSB could be construed as a precedent for including JLA stories.
I checked and Fleischer does indeed list All-Star Comics in his abbreviations at the front of the Great Superman Book. However, in the entire run of AS (at least in the time period covered by Fleischer), Superman made only two appearances, one of them a throwaway cameo in #7, and the other -- the only one that could really count as a Superman adventure -- was issue #36, wherein Superman encounters "The Wrecker," a man turned evil by the Stream of Madness, Koehaha. I looked everywhere I could think of in Fleischer's book and there is no reference to the JSA, Koehaha or this version of "the Wrecker" (though there is an entry for another character by that name).
Thus, unless someone else knows where Fleischer actually references an All-Star issue in the body of the encyclopedia, I'm inclined to rule his inclusion of All-Star on the abbreviations page irrelevant to this matter. (Incidentally, he also includes "Superman's Girlfriend Lois Lane" -- but not "Superman's Pal Jimmy Olsen" -- and "Limited Collector Edition", though again I do not see them referenced in any entries in the book).
Also it should be remembered that JLA began its run in 1960, well within the period covered by Fleischer. If he'd wanted to include JLA stories, he would have.
So...I'm inclined to vote "no" on the Superman of Earth-A since, in my view, he's not nearly important enough to justify a precedent that would open the door to every JLA story.
On the other hand, it could well be argued that since Fleischer included All-Star, it means he considered those stories part of canon, even if he ultimately forgot to include the actual stories. And in the same way that we have adopted to our "canon" list Lois Lane and Jimmy Olsen issues -- which like AS, Fleischer included in his abbreviation while never (unless I missed something) referencing them -- we might also adopt All-Star Comics to our list as well.
Seeing as how the book resumed publication in 1976 and soon featured you-know-who rather prominently, this would give us an opening to flesh out the "Superman of Earth-2" entry.