Yes, the other two Pokemon in the team must be good for it to work, but even if you had three fast, frail sweepers, you would run into a problem which a SR-lead alleviates (Spelling fail I think): Focus Sash and Sturdy Pokemon. Frail sweepers would get a hard hit in, hit the opponent down to their Sash/Sturdy, then the opponent would either get a lucky hit or kill you outright due to your frailty. With SR up, though, your sweepers can, well, sweep without worrying about Sashes/Sturdy-abusers.
Basically, you're using a slot on your team to protect your teammates from being "one-turn-revenged" (A term I made up to describe when an opponent lives due to Sash/Sturdy, and proceeds to kill your Pokemon in the same turn) so they can successfully sweep through the other person's team. Also, you're probably gonna want to use a Special sweeper and a Physical sweeper, like the person that thought of using Skarmory suggested Garchomp and I will too, and I will also suggest Specs/Life Orb Starmie as your Special sweeper, which resists Ice for Chomp (even though neither of them can take a hit, a resistance is nice) and Fire for Skarmory, while Chomp resists Fire (for Skarm) and has an immunity to Electric (for Starmie and Skarm)
A lot of strategies look or seem very good, then you lose a few times. I really recommend just playing a bit and going from there because with all due respect, it seems as if you don't really understand what these 3v3 battles are like. You want most wins to be 3-0, 2-0 should be a "close call". You can't afford to continually put yourself in situations where one crit, one hydro pump miss, one flinch, loses you the match. It's fundamentally different than 6v6 against another player. The AI just wants to knock out each pokemon in succession, it will not consider the match as a 3v3 but 3 lots of 1v1s (like bad players do), it's exploiting this programming that ultimately leads to very good strategies - such as trick scarf.