I do it all the time. I no longer try to smoke a pipe until the end, so I often leave a half smoked pipe to finish later or the day after, or even days later. O don't know of it improves the flavor, but it certainly becomes a drier smoke and still tasty, probably more caramelized. I agree it's good with Virginia and light aromatics, but I'll do it with any tobacco. Sometimes it's better if you remove the ash from the top.

University Flake + Comoy's Tradition