I have never been able to join files with differing formats. Try it yourself and see what happens. The program will just refuse to even start the process, in my experience.
They have to be more than just in the same format--they have to agree in other areas too--frame rate, sound, etc.
You lose a little bit of quality when you convert, but it might not be noticeable to your eye.
If you go out and shoot a video with a camera, it's no problem to cut out a section of it and then join the remaining 2 parts---it's easy because that video is all the same format, sound, frame rate, etc. Machete Lite is a great program for that, but it does not convert and it works only on AVI and WMV files.
But if you have 2 video clips from 2 different sources, they will probably differ in several ways, so you need to convert something.