Yes, slurred speech can be a fibromyalgia symptom.  FM patients often report a number of cognitive functioning problems including memory loss, difficulty concentrating, slurred speech, transposing letters and numbers, inability to think of the word you're looking for, thinking one thing but saying or writing something different, etc. 

I can't say for sure, but I suspect that when we're stressed – like on a particularly painful day – our cognitive functioning abilities are probably affected more than usual.  Of course, if the slurred speech gets worse or you have other new symptoms, be sure to see your doctor right away to make sure it's just the FM.