1. the exact results might depend on the scope(analog vs. digital for example) but in general you'll get aliasing. The display will be erratic, show the wrong frequency, and not be very useful (could be misleading if you are unaware that you've exceeded the sampling rate!).
2. Not very clear what you're asking. assuming this is a digital receiver, if the input signal is ugly but within required limits, it may still hurt your system's robustness / error rate by reducing margin against other noise, and by adding excess noise to the power plane and / or nearby signals.