Would finishing an entire course about C# at HomeAndLearn.co.uk and then jumping into XNA be a wise path to take?
Ultimate goal is to create a multiplayer 2D game.
Since I have never taken those courses, I can't speak for that site. However, I can tell you that no amount of classes or lessons will compare to experience. The best way to learn is to jump in and do stuff.
C# is a pretty easy language to pick up. There are plenty of sites that offer tutorials free. Also, XNA is just a library that sits on C#. There really isn't any reason why you can't learn C# by making simple games.
Start by making something simple. Maybe a static sprite that moves across the screen when you press certain buttons. Add some objects to play with collision. Then when you feel comfortable with that work on sprite animations, and a simple camera. It really isn't hard.
If you want a jump start, look at something like Flat Red Ball. It is simple 2.5D game engine that might help. If you want to make your own, look at this tile engine series. It will show you stuff like how to make a camera, animations, collision, and the rest. There is also this 2d tutorial series. I don't have a nice playlist for it so you will have to search youtube for the different parts. For even more resources, check out the ever-growing list of samples on the App Hub site.
If you really want to take classes, I can vouch for http://LearnVisualStudio.net. I know a few people who have taken them, and have seen the content. It is presented nicely and easy to follow.
When in doubt, come back here and ask questions. The people here are very responsive and helpful. If you need help on general C#/programming concepts try http://stackoverflow.com. It is another wonderful resource.