and even if your using units against their counters (fighters against flak) they can still win -- it requires a fair bit of numbers, but nothing to overwhelming.
Actually if you use fighters against flaks, you need hundreds of fighters for some few flaks.

Although with bombers, that's a bit more likely.
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But no, throwing hordes of ships at a human enemy will eventually get you killed, since she would probably either have overrun you before your economy is up, attacked your back while your ships where attacking in front or shred your ships to pieces with defenses and capitals.
Or something totally else.
That doesn't mean that Sins is balanced at the moment. It's not. But we aren't in the gameplay beta now, so expect lot's of tweaks in the next beta.