We don't know, but there's no reason to think not.
There's not much canon information on the precise administrative workings of Gringotts bank. You can find a detailed analysis in this excellent answer, as well as a small amount of canon information from the old Pottermore in this answer to the same question.
But we do know that goblins are willing to lend money to humans:
"Lee Jordan's dad had had a bit of trouble getting money off Bagman as well. Turns out he's in big trouble with the goblins. Borrowed loads of gold off them. A gang of them cornered him in the woods after the World Cup and took all the gold he had, and it still wasn't enough to cover all his debts."
-- George Weasley, HP and the Goblet of Fire
Whether the money Bagman borrowed took the form of an official loan from Gringotts or just some cash from some dodgy goblins he met down the pub, we don't know. But certainly there isn't a general goblin policy against lending money to humans - it's something that they're willing to do, and they might well do it through the official channels of Gringotts too.
So I would conclude that the answer is probably yes. Things don't generally seem to work differently in the wizarding world from the Muggle world unless there's a particular reason for them to do, e.g. one related to magic usage or magical creatures. Goblins aren't a reason for loans not to be a thing, and nor is the magical creation of money (by Gamp's Law of Transfiguration), so the default assumption is that Gringotts probably does do loans - at least, we have no reason to think otherwise.