Semper Fi: The Imperial Legions – while obviously there is no direct causal connection – do have many things in common with the Marines. (Apart from the obvious troperiffic ones – yes, we all know they’re a Proud Soldier Race all their own, commanded by Colonel Badasses, the truest devotees of The Spartan Way, and almost a Church Militant… although they’re more Warrior Poets than Blood Knights (except the kaeth… no, even the kaeth), lack Drill Instructor Nasties for the reasons suggested under Mildly Military, and most of their commanders, at least, aren’t General Ripper. Except for the Sargases, as usual.) Certainly aspects of the attitude and the mythos.
But also, despite their origins in the army of a land power, in later days (due to that land power allying with a major sea power) they did do most of their fighting as an amphibious rapid-reaction force, and, of course, when the Empire went into space – see, obviously, Space Marine – as the orbital equivalent of such a force. And since imperial annexations of anything resembling a major world work very badly across interstellar distances, most of the Legions are optimized for a similar rapid-reaction, tip-of-the-spear, in-and-out role.
So differences in culture and tech aside, they’d probably recognize each other, I do believe.