Hi there, quite a few questions here, but I think they all come back round to the same point.
The point being that Google does execute basic Javascript on websites. In particular, if you're using a method like this then Google will execute it:
document.write('Go to this awesome service');
There's a good write-up all about how Google executes javascript on SEOMoz that I urge you to read for more detail.
With that considered, then the answer is that that link on each site would benefit you and you are in effect forcing people to give you a backlink.
I'm not so sure this is a dreadful thing though, you're providing a free service and the link is relevant to the context in which it's being used (presumably).
I guess the thing you need to ask yourself is whether people from 'bad neighbourhoods' are likely to use your code? If they are, you may wish to do a nofollow tag here and rely on other methods to build links.
Hope that helps!