I have a 1969 Columbia Newsboy Special that I have had for many years and I have never replaced the tires. Got the bike out of the garage and pumped up the tires to ride and the front tire poped. Rear tire still good. Will replacing both tires depreciate the value of the bike if I ever decide to sell it?
In my opinion the original tires would only matter to a very small segment of the people, and only then if it was considered a "museum piece", and what are the odds of that? You could always remove the tires ( and possibly wheels ), and replace them with a functional set of wheels and tires, and store the originals if you feel the need to keep them around. Rubber tires don't last forever and will continue to degrade even if stored in a basement. I've been through the Bicycle Museum of America that has an extensive collection of bicycles from the late 1700's to present. Many of these bicycles have parts that aren't original due to accidents or simply being used up over the years they were ridden, but that certainly doesn't detract from their historic value. Wooden wheels and solid "rubber strips" for "tires" didn't last long on the roads they had in those days. Repairs and replacement parts are a part of the history of that particular bicycle.
Like any antique, the closer it is to "original" the more likely the value will increase. However, in the case of many items, there are parts that wear out or decompose over time (rubber, wood, even metal) so they are expected to be replaced.
Now, what you could do to maintain value or at least attractiveness to a potential buyer would be to replace the tires with newer versions of the same tire, or try to find ones that look similar to replicate the same look of the entire bike.
The tires shouldn't have an impact on the value of the bike. Tires wear out and are discarded. If you are concerned, though, and you plan to ride the bike, replace the tires with new ones and keep the old ones somewhere so they don't wear out further.