The RS300 is an FM. For FM and AM the wire length is matched to the frequency of your crystal. Any mismatched antenna length runs the potential to lose distance or get increased interference which = bad mojo.
You can see how this is calculated
here. If by "taping it back together" you mean you reattached the antenna wire so there's contact you should be okay but if you haven't soldered/reattached the wire connection and you've lost some antenna length, you can use that site to cut your antenna to a correct length for your frequency. That will reduce frequency interference but bear in mind that your overall range will be less. You might as well just get a replacement, they're cheap