I think so too. I mean, you'd have to be careful with how you say it, of course, but you should.

So maybe you go about it by acting like you just assume that'll be the way it would happen, because of course you'd be classified as a full-blooded wizard, you're only keen to know about whether you'd get a foster family or not due to your unique position. And I wouldn't even mention the possibility of being classified as half-blooded as a deal-breaker. It'd be implied well enough.