You won't hear anything from an unmodulated carrier, the mixer output would be DC.
The reason for being so cautious with answers is it sounds like you are expecting to make a receiver with some vital parts missing. You have to bear in mind that if you (example) receive a signal at 500MHz and mix it with a 500MHz LO, the output will not be audio, you get any deviation from one signal to the other, such as phase and minor frequency shift instead. Any modulation on the signal will also produce two products, LO+modulationl and LO-modulation which may be difficult to utilize. That is the primary purpose of using an IF, it keeps the products apart in the frequency domain so they are easier to filter.
However, for some signals it may be possible to directly demodulate into in-phase and quadrature (I & Q) signals using two mixers but to do so you have to consider how to produce the 90 degree phase shift over a wide frequency range.
I would suggest if you want to do some inexpensive experiments, you buy a DDS frequency generator board from a well known on-line source and first experiment with mixers over the frequency range it can produce. Afterwards, you can substitute it with a PLL to widen the tuning range.
Brian.