Will A new DAC improve the sound of my Cary 306/200 CD Player

I have a Cary 306/200 CD Player which I purchased in 2003 for about $5000.00.
I am happy with said player, but would it make sense, since DACS have vastly improved over the past few years to
bypass the current DAC and purchase a DAC, in the $1000.00 range, such as the Mytec Liberty Dac to improve the sound. I am happy with the transport and my rationale is that for $1000.00 or so, I can essentially greatly improve my sound for a modest investment. Appreciate any recommendations, as well as any thoughts regarding my reasoning. The
question is would bypassing the old DAC with something up to date, make a big difference therefore justifying the
expense?