As to the question: Yes, if you download 10% of the tiles, they're still there. When you re-start, it will skip downloading those tiles as it hits them. At least that was true the last time I used it, to grab tiles. I cached 90% of the area I usually am in, and rarely get tile traffic because of that now.
12Mbps wifi but downloads are very slow, maybe lots of computation or maybe openstreet limits the download speed a lot.