haha, interesting question, I'm not a princess sadly, but I am an Arab ;)
Either way sure, why not? it's different according to the woman though.For example, My friend wishes to marry an American Muslim( it's like her dream!) lolz. A casual relationship? you mean like just friends or more? Again it's according to the woman, if she's conservative or more open minded, I can't generalize here.
Well, I hope I helped in some way or form :P
lol, Good luck!