There is no way to answer this question accurately without knowing a great deal about the specific situation involved. Employees are more likely to obtain the concessions they want from their employers if they have leverage. This is what determines whether employees should strike.
A group of employees has leverage if the management of the firm needs those workers more than the workers need to be working. If the firm is in financial difficulties, for example, it may need to keep putting out product so as to avoid falling into further financial troubles. In such a case, the union will have leverage. If, on the other hand, the firm is on a solid basis, the union will have no leverage and should not go on strike.
This is the sort of calculation a union must make. It must decide whether a strike will hurt the workers more than it will hurt the employers. This is what determines whether a strike is a good idea.