Suspect it wouldn't work very well and possibly not at all. There's two parts to upsampling. The 16 bit conversion to 24 bit word length and the 44.1KHz sampling rate conversion to greater than 88.2KHz. An older DAC may not accept a signal any higher than 20bit @ 48KHz. The DAC would probably just ignore any bits after the first 20bits and simply truncate the longer word length, but it won't lock at all to a higher sampling rate. You could always set the upsampler to perform only the word length conversion and leave the sampling rate unchanged. But why bother, I recommend you either get a more modern DAC (one that accepts a 24/192 input signal), or better still get a DAC that has built in upsampling capabilities.
BTW, there is a sizeable group of audiophile who say upsampling degrades sound quality.
BTW, there is a sizeable group of audiophile who say upsampling degrades sound quality.