According to the OED, the original meaning of the verb rape was simply to seize by force – nothing about carrying off. You can, for example, “rape” a location in this sense. There’s a cite from ?1387 which uses “rape” to refer to the eating of prey by a carnivorous fish.
The “carrying off by force” sense is identified by the OED as a distinct meaning, with the first cite from 1450. Apparently this sense was, from the outset, used especially (though not exclusively) to refer to carrying off women for the purposes of sexual violation. Note that the act of rape was the carrying off, though, and not the subsequent sexual violation.
The third sense of actually committing sexual violation, with or without any preliminary carrying off, is first cited in 1574. But, interestingly, this sense disappeared in the 18th century, and didn’t reappear until the nineteenth century – the OED has no quotes between 1684 and 1823.
According to the OED, the third sense is “now the usual sense”, to the extent that it influences the other two senses. But the first two are not obsolete, and the OED has modern quotes for both of them.
Twentieth century citations from the OED for “rape” in the sense of carrying off by force:
1934 - (The Times, 14 February): “Not a day dawned in the dry season when a pagan could be sure that he or his womenfolk or his children might not be raped away to slavery before the sun went down.
1989 – (K. Rexroth, More Classics Revisited, i. 9): “Phaedra, after all, is a princess raped away from the old decaying Minoan civilization of Crete by Theseus, the representative of barbaric Athens.”
2003 (The Independent, 30 December): “Nearly a million of those burnt and raped from their homes during the war have gone back.”
As you can see, in each of the citations there is at least some suggestion of the possibility of sexual violence. Nevertheless the focus is on carrying away.