I haven't been able to use my d/l manager with SBB, since the cart (and now the freebies section) encrypts the links. Kind of a bummer, but I will find a way to make it work.
I use ReGet Deluxe, and IF the site supports it, it will resume where it left off. For most sites it works, there are a couple I've come across that it doesn't work and I end up having to start over. To combat that, though...I set it up to download at night, and don't have problems with it shutting down on me or anything, most of the time.

But to resume, I can't just tell it to reconnect most of the time...I have to go find the link and click it again, then tell it to start and it "knows" when I've already downloaded part of the file and picks up the zip in it's folder and continues downloading to it. It's SOO nifty. I love it!
Oh, and for me, it definitely accelerates my downloads. For a person not on dial-up they'd think I was crazy when I get excited about my speeds, lol. Downloading through my browser, the best I can get is 4.5 KB/sec. With my download manager, I get up around 6, and sometimes it jumps between 6 and 10. Still not REALLY fast, but the benefit for me is that I can schedule it and download at night, tell it to shut down my computer or internet when it's done, etc. And I don't have to worry about what will happen if I lose my connection. If I was using the one in my browser (which I've done) I have to sit there and babysit it while it downloads or it screws up and I have nothing but problems.