As you are planning a long night-time exposure, there will be little risk of introduced vibration during the actual exposure. Problems I have experienced with star trail photography are numerous and unique e.g. animals wandering about and colliding with the tripod, spiders seemingly finding their appearance attractive and making the front of the lens a looking-glass, condensation on the lens, wind and then clouds. You really do need the moon and stars to be aligned 'just-so', and once that is done, worry about MLU...
OK...The primary purpose of mirror lockup is to reduce (but not entirely eliminate) vibration caused by the abrubt movement of the mirror swinging up, then the shutter opening and closing and the mirror returning to position; that is to say it isn't just the mirror, but also the shutter that plays into the equation, and big focal plane shutters cause as much hue and cry as the equally big mirrors. If the camera you use has a reputation for introduced vibration from mirror movement (e.g. Pentax 6x7 / 67, of which chapter and verse has been written and repeated ad nauseum), it is a priority for slow speeds. There are many additional tricks to apply additional to MLU to prevent vibration, which chiefly will be noticeable below 1/60th.