There is a bit controversy in the industry as to what exactly a web designer should know. Some people say knowledge of HTML is essential, some say it's not necessary at all.
My take on it, as a web developer, is this. You should know *some* html.. at least the basics. I don't think it's as important these days, because.. well.. Okay.. Say you're a web designer for some company and you have just met a client and are working on a look and feel proposal type of graphic for them. You're working on one .jpg - a look and feel mockup of what you propose the final product should look like. You meet with the client again and you go over what you have produced - the client proposes changes, and you implement them and go through the process again.
Eventually you will have something the client is happy with. Now.. in the past, web designers would then splice up their proposal .jpg into individual parts and produce the html that "holds it together". They would stick all the component pieces of their design (the logo, content area, menu, etc.) and put it in an html table. HTML knowledge is a requirement for this part. HTML tables are fairly simple to work with, so web designers did this part and nobody cared.
The thing is that nobody uses HTML tables for this purpose anymore.. or at least they shouldn't. It's very frowned upon. A good site layout will use DIV tags. You need indepth CSS knowledge to accomplish this. Is this the job of a web designer or a web developer? Or somebody else entirely? That's the "controversy"
So to answer your question, it really depends on what you want to do with this. Do you want to work for a large company? I would focus on the graphic design aspect of it - and get better at that. Learning the basics of html and css would help - but probably mostly with the hiring process (i.e. it would look good on your resume, etc.)
Do you want to do freelance graphic design work? You will need to learn html and css.. No question about it. There will be no web developer there to help you, so you'll need to know that stuff.. Even if you partner up with a web developer - you'll be working as a team so you should have a decent knowledge of html and css.
