No. First, miners aren't linked together in the way you mean. Sure, they have mining pools of their own, but each mining pool provides its own parameters to its miners.
Second, ASIC miners are designed to solve a VERY specific problem. Most are designed for a block header of a very specific length (80 bytes AFAIK) to be hashed twice, with one part of that block header incrementing, and the output being fed to a comparator to the target. They can only solve one problem, which is the problem they're already solving. Find nonce and extranonce such that block header containing transactions and coinbase address of the pool in question, when hashed twice using SHA256, has a value less than a fixed target value.
Of course, they do solve one other problem. They heat rooms.