Run an atmega328 only using an 16Mhz crystal without caps
If you mean a two pin crystal like this one



then the answer is no.  This type or crystal requires the two capacitors in order to oscillate.

On the other hand if you mean a 4 pin crystal oscillator like



then it can work fine because this is a complete oscillator that only needs power to generate the clock.
In order to use it you have to set the clock source of the AVR to external clock (CKSEL3..0 = 0000) and feed the clock signal to XTAL1 pin.