Actually my feeling is that if the single player is glorious the multiplayer should probably be fine too, but the other way around I am not sure. You can get away with multiplayer a lot better than with single player, in my experience, since a good AI is one of the toughest things to implement and as it is now in ELEMENTAL the AI is just unable to do all the stuff players can do.
How so? Large swaths of the SP game simply don't exist in MP. Lets say FE boasts major improvements to tactical combat due to the unit skills and such. Since tactical combat itself doesn't exist in MP (it's auto-resolve only), there's no change at all in the MP game despite that improvement in SP.
Personally I believe that spending more time perfecting the multiplayer would improve a lot the lifespan of the game, that would mean fixing bugs, adding a play by email option and balace spells. Also making certain things optional, so that player would be able to customize their games would help.
Perfecting the single player on the other hand would mean to teach the AI how to use spells and skills as well as players do, which is a real tough thing to do. As stated in other posts even Age of Wonders Shadow Magic (IMO the best game of this genre yet), shows lots of flaws in what the AI can or cannot do (and believe me the developers of that game worked hard and well on the AI, which is quoite challenging in fact). The fact is that after a while even the best AI can be anticipated! Should the AI units come out of a city when the enemy armies enter their empire or should they not? Should they all regroup in the main city to sustain a huge attack or spread around and try to defend all cities with equal defending forces?... All these strategic choices are so hard to make even in real time and even for player who know their opponent, how can we expect the AI to have the right formula each time? In AOW units regroup in the main city, but make quick attacks to approaching enemies if they feel those enemies are weak enough... Is that always the best tactics? Sometimes approaching a city with a weak force is a strategy to catch the enemy off guard... and so on...
In Elemental at the moment we are far from that in terms of AI (haven't tested 1.3) - Even in tactical battles teh AI seems to keep attacking the closest enemy even if it has a huge amount of defene and will almost certainly destroy them...
Realistically the built in audience for these games is primarly SP. If the SP game is fun, you might be able to lure some of those people online for MP games. But if people try it in SP and find that it's still not fun? They're going to play something else, not jump into MP.
AI is also something that MP would benefit from because coop is a popular form of MP game... except that WoM also doesn't support coop or AI players in MP.
The path here is pretty clear. If they want to improve MP, what they have to do is bring it to feature parity with SP. At that point it simply inherits all the improvements being made in FE for SP, which will boost MP as a bonus and gives SP players a reason to try it (a better challenge because humans > AI). What they have right now for MP support is "WoM-Lite" and that's just not worth caring about. Trying to change it to balance spells or what have you won't help it because the game itself is a weak version of WoM. There's no reason for SP players to want to try a weaker version of the game, and there's no reason for MP players of other games to want to come here when they have better options elsewhere.
I've said it before and I'll repeat myself - FE should either bring MP up to feature party with SP (so we're playing the same game), or they should just disable it entirely and save QA & server costs. The status quo simply isn't good enough to be worth keeping (and seems to primarily exist to tick the box saying "yes this game has MP" in reviews).