Because smoke ring and smoky flavor are two completely different phenomena, the simple and straightforward answer to this question will always be "no." a chunk of meat without a smoke ring can taste better than a chunk with a smoke ring. The reason behind this is that smoke rings develop from the reaction of gases present in smoke with the protein myoglobin present in meat. Myoglobin content differs from meat to meat, and thus, a meat with higher myoglobin content can have a smoke ring with the least exposure to smoke. Smoke contains different gases like CO and NO which react with heme present within the myoglobin. This reaction gives a pink color to the meat known as "smoke ring". Myoglobin breaks down at 76 °C (170 °F) and the smoke ring stops expanding. Red meat like beef has a higher myoglobin content than white meat like chicken. So beef meat can develop a smoke ring quicker than chicken meat despite being exposed to smoke for the same amount of time. So we can't judge a meat's flavor by its smoked ring. While the flavor of meat comes from its exposure to smoke, The longer a meat is exposed to smoke, the more intense the smoked flavor. So a meat chunk can be exposed to smoke for a longer time to produce a smokey flavor even without the development of a smoke ring. A smokey flavor develops from the gases present within the smoke. So it is affected by the wood being used. So it's better to choose the appropriate type of wood and use wood with mild smoke after some time to avoid the bitter taste. Choosing smoky flavor from smoke rings is a common misconception, and it arises because of a correlation between smoke rings and smoky flavor. The reason is that if a meat chunk has a good smoke ring, then it means it took a lot of time to reach 76 °C for the breakdown of myoglobin. which also means that the meat should have been exposed to smoke for a longer time. So smokiness is related to flavor to some extent, but it's not the best determinant of smoky flavor. You should consider smoking at a low temperature to get both a smoky flavor and a smoke ring at the same time.