Does blocking/countering do damage in Arkham Asylum?

I’m currently in the room where there are a dozen or so thugs searching for something. I’m playing on Hard for the achievement and I’ve spent hours trying to beat them all.

After dying many, many times, I’ve decided to just block and maybe throw a punch if nobody’s nearby. I didn’t realize the necessity of good combo moves so my upgrades are useless.

I’d just like to know, am I wasting my time? Does blocking (where Batman grabs their fist and twists their arm, elbows them, punches them, etc.) do any damage? And does that mean I can just block each enemy 14 times?

I’m playing Batman: Arkham Asylum on the PC if that matters.