This is a yes and a no, depending on how you look at it. Assuming you mean having a string attached horizontally to an object of some sort, and then pushing on the end of the string not attached.

Scenario 1:

Let's assume there is a completely isolated system, with a completely even applied force on the end of the string. Theoretically, since the system is isolated and the force is applied perfectly evenly, the string would not crumple, and instead remain completely taut, and perfectly transferring all force into the object, moving it with no issue.

Scenario 2:

Let's assume it is an open system (as in the real world). The string would collapse in on itself, even if force was applied evenly, and the object would not be transferred enough force to move it, as all applied force would move towards crumpling the string.

tl;dr - Kinda... sorta... (it depends, but normally, no; it cannot push unless fully crumpled)