Yes, you can do it, somewhat. You can draw a black'n'white mask on usercontrol that gives you a flat transparency. Alpha transparency is not possible (easily). Having such a mask also has some limitations and the end result will be much heavier than the regular line control, so it doesn't really be very useful of a control. As, it won't work with two end point mechanism, it'll always be a rectangular shape that you draw with a usercontrol (so you have to have a property that tells which corners the control should account for).
Anyway, define better what you're after and you'll probably get a bit better answers
LaVolpe has AlphaImage usercontrol that is able to display alpha transparent PNG images, which also allows for rotation. Pretty cool stuff, the project is a bit big and complex though.
Nope, you're not getting that. It would require hacking & testing all too much to get such a simple effect and working it in a stable way, you probably can't find anyone that skilled to work with VB6 anymore.
I'm trying to make a user control like the one you want to make, because I need it to implement a class diagrams application. The best I could find is this: