Semper Fi is probably going to be the Marine Corps' watchword forever. It's one of the best mottoes ever.
Yes, but the Imperial Marines are not the US Marines.
Let me say, first off, that it's certainly
possible that the IM's motto is the same as that of the US Marines. If, somewhere, there's a canonical statement to that effect, that can be explained by tradition.
But absent that, I'd say that it was unlikely.
GT:Ground Forces states that the IM "can trace its lineage back to the Terran Confederation Marines" and mentions a number of traditions (See p. 34-35). The motto is not mentioned (unless it's somewhere else in the book). Significantly, the IM is not said to trace its lineage back to the US Marines. Yet surely the TCM must have included a number of transfers from the USMC when founded?
I'm fairly hazy about Terran Confederation history, but ISTR that its member nations continued to have a separate political existence, as sovereign part of a federation (at least formally). This suggests to me that the TCMC and the USMC would exist simultaneously. That, and the fact that the TCMC would have recruits from all over the world, further suggests that its motto would be something different. Deliberately so.
So what would the motto of the TCMC be? My guess would be some soppy humanitarian United Nations-type sentiment, like "Always Helpful" or "United we stand" or "Always Together" (properly latinized, of course). Or perhaps some sort of jingoistic "Terra Über Alles" thingy, though in the latter case I'm quite certain that the motto wouldn't be one of the traditions that the Imperial Marines would adopt.
Whatever the motto of the TCMC was, there's plenty of time and plenty of successor organizations in between (Rule of Man Marine Corps, Sylean Marine Corps, Federation of Sylea Marine Corps) for the Imperial Marines to have an altogether different motto.
Hans