those bits need to be converted into an analog signal.
There are several ways to do that the common cheap solution is what’s called a Delta Sigma DAC, in theory this involves modulating a single bit at much higher frequency than the sampling rate. In practice some of the top bits are directly decoded using a resistor ladder. But to do this the input signal needs to be both over-sampled and filtered (different DAC’s do this differently).
In addition you don’t just squirt the output of the DAC chip onto the RCA connectors at the back, there is an analog filter (to remove the noise the modulation introduced) and there is an amplifier in the DAC.
So even DAC’s with the same DAC chip will sound different.
Most cheaper components pretty much just build the circuit in the manufacturers data sheet, and in some cases expose the various digital filter options the underlying chips provide.
As you move up in price point DAC’s can use custom digital and analog filters, do custom oversampling etc etc.
So yes they can sound different.