There's no direct advantage to playing a weaker deck. There is, however, an advantage to managing perceptions.
In some sense, free-for-all is about always being outgunned: taken together, your opponents have more resources — more cards, more mana, more life, more time (turns) — than you do. Luckily, those resources aren't always directed against you at all times. However, as The Ferrett says, "Eventually, you have to be Alpha Threat to win" — and, when you are in that position and most of the table is gunning for you, it pays to have access to strong cards that can power you through that opposition.
The flip side is that those strong cards are more likely to get you labeled as the "Alpha Threat" prematurely. The best way to mitigate this isn't playing weaker cards, it's good strategic timing: as he continues, "The lesson is that you have to time your shot at dominance perfectly. You have to wait until your opponents don't have the resources to stop you, or you have the ability to stop them."
Multiplayer strategy writers emphasize the importance of gaming your opponents' perception to get to that point. Your card selection certainly plays a role here:
- Even if you're just defending yourself, too powerful of an early board presence might make your opponents see you as the major threat. This could be an argument for playing bad cards, but...
- Inversely, too little of an early presence marks you out as an easy target — some players love to take pot shots at anyone who doesn't have some blockers — or, worse yet, gets you flagged as That Guy Biding His Time Until He Can Use His Combo, at which point many players are likely to move to take you out even if you have no obvious strength, based on the fear that you could steal the game at any time.
- Some players just love to "spread the love around," e.g. by attacking a different player each round, largely independent of their relative standings. Moreover, lots of multiplayer cards affect all players at the table: you don't have to be "The Threat" to have your carefully-laid plans trampled by another player's Cabal Conditioning. A weaker deck may dodge opponents' direct attention but find its game grinding to a halt anyway because it can't recover from collateral damage.
Thus, depending on the group, appearing weakest may be an advantage, a disadvantage, or largely irrelevant. Strategy writers often advise hiding your strength without actually showing weakness — trying to keep yourself in the "middle of the pack" to avoid the undue attention that may come from being either on top or at the bottom.
In my experience, the best way to dodge attention in multiplayer, particularly with relative strangers (e.g. at a game store rather than an enduring kitchen-table group) is not so much to play a deck that appears weak as a deck that seems linear and predictable. Players tend to spend most of their energy worrying about decks that threaten to do big "broken" game-changing things, or decks whose gameplan they have yet to figure out. Thus, it pays to play a deck that can build up in a slow, measured way with a very "obvious" gameplan, like creature-based midrange beats. Even when opponents notice your buildup, there's a bit of a tendency to dismiss it as a problem they can deal with in a couple more turns, after whatever more pressing concern is addressed.
My wife often steals games this way. She develops her board with some decent creatures, goes after one or two of the weaker players while the big splashy decks fight each other, and then sticks a card like True Conviction or Bellowing Tanglewurm for a game-winning alpha strike once the coast is clear. To win this way, you actually need some of the attributes of a strong deck, just in less "sexy" categories like consistent development and resilience. A deck that's straight-up weak across the board can play the same unassuming startup, but won't be able to capitalize on the late-game state in the same way.
Does her approach win a disproportionate amount of games? It's hard to say with certainty. She seems to win more than her fair share of games, but I do, too, with much splashier punch-everyone-in-the-face control decks. I think trying to be unassuming and predictable works best when there are several big decks fighting for supremacy, e.g. with lock pieces, serving as a suitable distraction for themselves and all of your other opponents; if the table just has one, that deck likely has the resources to run you over while you're still in your "slow and steady" mode.