According to BioWare, it is possible (spoiler-proofed caveats below). I know that I refused to do any of the multiplayer/mobile stuff, and I probably came very close to the maximum number of "points" without doing anything but the single player game (I tend to play slowly and ensure that I don't miss anything, restore from saved games if I make a mistake that doesn't seem likely to give me a good outcome, etc.).
Having said that, the "endings" are sort of hard to describe in terms of "the best", etc. From what I've read/YouTubed, there are cases where if your score is "extra high", you get additions to the main ending scenarios (in terms of extended cutscenes). I did not see these in my play, but did see them in YouTube clips from folks who said they'd done the multiplayer/mobile stuff to enhance their scores. Someone did a pretty thorough analysis of endings available at different point scores, and some of them were available only if you had a *lot* more points than I did (which would absolutely require the multiplayer stuff).
But the differences were minor. This is likely what BioWare was referring to -- I do believe that you can get the "main" endings without getting those multiplayer points (multiplayer/mobile stuff can *double* your point totals). But you may not be seeing quite all of the content of the "best" outcome cutscenes.
But really... as you've probably noticed in the comments here and elsewhere, this is not a game to play for its ending. I found it a great game, with an enjoyable storyline up until the end -- it was certainly worth it. If you liked the others (especially ME2), you'll probably like it. Except for the ending -- but don't let that spoil the 98% of the experience that is great.
And yeah -- I had no desire to play the multiplayer either. I remember reading something a while back, when EA bought BioWare, that said that EA was mandating that all of their games have a multiplayer component (Boo!), which is what resulted in what is apparently a very tacked-on multiplayer component (even though I've ready that some have said that it was well done and pretty fun, as such things go). I still don't really have any desire to try it.