Unlikely to cause damage. MAYBE malfunctions like freezing up. But first, watch the PSU fan and see whether it does come on as the unit warms up, or never does.
Among PSU's with self-controlled cooling fans, I have seen two types. One runs the fan most of the time, from slow to fast, depending on temperature which is determined by system workload. The other actually keeps the fan off completely until the PSU gets to 30% to 40% of its capacity; THEN it gets warm enough to start the fan slow, and will speed up more if needed. I do not know which type yours is - the website does not say.