Can alcohol abuse cause widespread joint pain?

Yes. Alcohol abuse can cause or aggravate several physical (and mental) symptoms.
Generally no. My concern is that there is another underlying problem that is causing widespread joint pain, such as lupus erythematosis or rheumatoid arthritis (or potentially hundreds of other conditions), and that the use of excessive alcohol might be making worse. In addition, if you are continuing to drink despite it causing you pain, you clearly have an alcohol problem. See your doctor and get help!