Absolutely. Sound is everything.
However, changing the finish of any sax will affect its sound. I have recently stripped the lacquer off a few of my saxes (as some of you may know) and can confirm absolutely that the sound has changed. Overall I would say that the tone is now a 'warmer' sound with less shrill overtones.
I once owned a 1930s French tenor sax (Cavore) which was silver plated. The sound from that was (as described elsewhere) 'silky' (!?) but there were areas where the plating had worn. I made the stupid mistake of sending it away to be re-plated. When it came back, it sounded dull, lifeless and 'boxy'. As they say: "if it aint broken...." Needless to say, I sold it shortly afterwards as, to my ears, I'd killed it.
But back to the issue of construction materials and finishes generally.
Over the years I have played a great many types of sax made of a variety of materials in a range of different finishes and can confirm that the resulting sound is very hard to measure due to 'possible' differences within makers, models and set-ups. However, from those that stand out, here are my personal impressions.
I once tested a selection of Mark VI Selmers. 1950s unlacquered; 1960s flaked lacquer and modern fully lacquered as well as a 'custom built' solid silver model. The silver one was made for a Middle Eastern chap and weighed as much as a fridge!. Apart from being unwieldy it sounded no different at the time from any of the others. Certainly no different as to cause a significant improvement. I do have to say though that the filthy brown ones did have a more 'complex' waveform, with a softer, darker sound compared to the modern ones which were brighter, most noticeably in the top end.
I have also owned several of the post-war plastic saxes known as the Grafton. Again, in a comparison test they sounded no different from any metal sax of the same era. The plastic seemed fully capable of producing a clear, resonant sound across its full range.
In some ways I agree with various previous posts: the individual players technique and expectations play a great part and in the hands of an experienced player, any horn can be made to bring out a variety of contrasting colours. I think that the most important factor is personal preference. I, myself, favour the older and dirtier looking horns. They bring an aura of 'mystique' like they have lived a life on the road, basking in dressing rooms in smoky clubs, lying on the top of grand pianos and being hauled around on a tour bus. They were there, and they have a story to tell. -in my imagination!
I feel that the worst 'age' for a sax is that point at which the lacquer is pitted, flaked or partly worn. That's like a teenager with shoulder length hair: neither smart and short nor fashionably long. Those are the horns that need a facelift. Mind you! I wouldn't dream of having them relacquered if they were a vintage model with beautiful engraving, as the process sometimes goes a long way to destroying the character. One wouldn't varnish a Stradivarius, or paint a Bechstein. (Or re-silver plate a tenor! grrr. )
Brand new, or carefully cared for horns look fantastic and sound just as good, if not better than older, more lived-in cousins, but for me - give me 'grunge' every time. THE most important thing, however, is how it sounds, and if that works for you... embrace it, and forget how it looks.