Not keen, sorry. I am not a big fan of unisex/could be a surname names anyway, but realise that lots of people like them. However, I just don't think that the style of those two names goes together at all.
Would you actually use 'Morgan Rose' as the name, or would Rose be a 'never referred to except on forms' type middle name. If it's the latter and it has special meaning for you, go ahead. If you'd use them together routinely, I am sorry but I agree with the comment that it sounds a bit like a character out of Mills & Boon.