Will slack in rack and pinion steering cause.

No, but a loose tie rod end can ALLOW some other cause to result in shaking. Causes of shaking include tire balance, bent wheel, broken tire belt, and misadjusted "toe", an alignment angle. You need to provide a lot more detail to narrow down the cause.

As Doc said, it will exaggerate a problem that was probably minor to start with but definitely something else is triggering it and taking advantage of the slop.