"At-will" work would imply that, yes, you can fire striking workers. I can see no more reason to prohibit this than to prohibit strikes in the first place.
I don't think you even need 'at-will'. Someone that is so blatantly not doing their job that they're not even showing up to work should be trivial to fire under almost any circumstances. ahomescu1's worry is pretty unrealistic.
In most European countries, employees carrying out a legal strike are basically impossible to fire legally until the strike has ended.
But at the same time, the conditions for when a strike is legal wary substantially, and strikes for wage reasons are generally restricted to periods during wage negotiations.