The Imperial Seal was important enough to be handed down from dynasty to dynasty, and generally all important posts received some sort of seal to legitimize their power. But the power of the Imperial Seal was put to the test when Yuan Shu received the Imperial Seal from Sun Ce toward the end of the Han Dynasty. Yuan Shu used the Imperial Seal to found his own dynasty, however local warlords took exception to this and allied against him because the Han Dynasty was still technically in power. Only when Cao Pi had both the Imperial Seal and the Han Emperor himself did he successfully overthrow the Han Dynasty to create the Wei Dynasty. It's the only moment in Chinese history that I know of where the seal was not in imperial hands.

So in short, it was important but it could not legitimize a dynasty on its own.