Can I ignore the Nyquist criterion?
You can only "ignore Nyquist" if you a-priori know that there is no higher frequency content (above your desired or required noise floor) that will alias down (or up!) to your band of interest.  But since your signal has content at and above half your sample rate, you will need to low pass filter that signal before sampling.

You will also need a sampling rate ABOVE 1000 Hz, if you are interested in a finite length of signal at 500 Hz.