Sure is used to signal consent, or to put it another way, willingness to go along with something. It's often used in response to requests for permission:
Alice: Would you mind if I take the car?
Bob: Sure, go ahead.
In the above, Bob is willing to go along with the proposition of letting Alice use his car. Bob is not signalling literal agreement with Alice's words, which is exactly what yes does:
Alice: Would you mind if I take the car?
Bob: Yes, I would mind very much. Take the bus.
Compare the following:
Alice: Would you mind if I take the car?
Bob: No, go right ahead.
In this case, literal disagreement has the same illocutionary force as sure, so we can see that yes and sure don't mean the same thing. However, the opposite might be true in another situation:
Alice: Would you like some cake?
Bob: Yes, I'd love some.
Alice: Would you like some cake?
Bob: Sure, thank you.
Here, Bob's willingness to go along with Alice's proposition has the same force as literal agreement. No would signal the opposite:
Alice: Would you like some cake?
Bob: No, thank you.
In other words, sure signals consent, while yes and no signal literal agreement or disagreement.
The implication is that McGonagall is concerned about Harry's living arrangements; she thinks it would be best for Harry if he were to live with a Wizarding family who could help him grow and nurture him in their ways and with their culture and customs. The family she imagines him with is clearly not the Dursleys.
So for the actual parsing of the sentence itself: she is saying "If you searched the entire world trying to find people who are dissimilar to us (us being Wizarding folk) you would not find anyone so dissimilar as the Dursleys."
She clearly thinks this is a bad thing, and implies that she would prefer he live with a Wizarding family.
Best Answer
Yes, here ‘I’m calling’ implies that Harry has already decided on calling You-Kow-Who by his name, and he's not going to listen to anything that Hagrid has to say on this matter.