It's not hard to add noise to the position of a curve:
We start with our curve. We need a seed for our noise, so let's use index (which is unique.) Because noise outputs colors in the 0,1 range, we'll vector subtract 0.5 from our output. We can use a vector scale node to control how much we want the noise to affect our position. Then we'll use a vector math node to add that noise into our position, and set position for the output.
I'm showing four curves. Two are subdivided default Beziers, one with bevel; the other two are the same curves, but with the noise shown added to their position via geometry nodes. Note that it is not currently possible to set geometry nodes modifiers to "apply on spline" like some other modifiers allow, so any modification here is to the output vertices (as should be obvious from the modified bevelled curve), and cannot be used to control a follow path constraint, a curve modifier, spline IK, and probably a few other things.