It's an interesting question.
The truth is that finding multi-accounters is hard. Really hard.
At our other title, Illyriad, we limit players to two accounts each, and have fairly sophisticated methods of finding people who abuse this - methods that go way beyond the simplicity of IP addresses and browser session IDs, and into the realms of comparing syntax/grammar/typing 'signatures', playstyles and a variety of metadata. We use propensity models and probability theory extensively, and we think our tools are amongst the most sophisticated out there.
However, we know that there are multi-accounters who go undetected, because they're willing to put in the effort and discipline to use a wide variety of tools, methods and circumstances to circumvent our detection methods.
This doesn't create a massive imbalance in Illy, because the game is actually quite difficult to play in terms of the sheer amount of management that needs to be done to run 10+ cities successfully, and only the fairly disciplined and dedicated multi-accounters survive the purges.
Detecting casual multi-accounters is easy. Detecting dedicated (and tech savvy) multi-accounters is more difficult. Botting is (generally) easier to detect than a dedicated multi-accounter, because even botting with some random factors built in creates a (machine-generated) pattern, and we pass our data through some very sophisticated machine-learning algorithms to give us 'botting propensity' scores for players.
However, I'm being frank when I say that it's a difficult and time-consuming battle to fight.
Now, that battle becomes simpler when you have a very involved 'hands-on' game like AoA, where flying in space requires skill, timing etc, as @IAMAGEEKYEY points out. It's going to be difficult to multi-account in the context of combat, and certainly it's part of our remit to encourage multi-player grouping! And spotting bots (of the auto-X in-combat type) i is also much easier if we look at outlier stats, compared to a comparable base. It's going to be easier still to spot botting in terms of other game transactions (such as marketplace activity).
However - and this is the key point - the best battle to fight is the one you can avoid. With the systems that we have, multi-accounters and botters do gain an advantage over other players, but only if they're willing to put the effort in themselves in terms of discipline and determination.
It's the grind that encourages most botting, and we generally don't want AoA to be grindy! By reducing the potential gain from botting (whilst still maintaining the risk of detection), we feel we can make botting a low-sum game. We'll never make it go away entirely, that's for sure.
On multi-accounting: well, given that you can only fly a single ship at any one time.... our current thinking is that we shouldn't care about multi-accounting, and should make that part-and-parcel of the game experience - so long as it's only one account performing an activity concurrently.
If players want to try out different styles of play and skill paths and specialisations - or simply want to metagame - then multi-accounting is both useful to the play experience, and highly difficult to detect from those players sophisticated and determined enough to circumvent it; so why not embrace multi-accounting, so long as it's not simultaneous? Botting will, forever and always, remain a no-no.
Would welcome feedback and thoughts.