Hi. I was just asking the same question and from what I hear they can. I know mine do. I haven't been diagnosed as of yet, but I can tell you if this is what I have then mine certainly do. Mine were horrible last summer (this is when I started to notice them significanlty and before I had any idea of what was going on.) I was on a downward spiral and about to lose my mind because I felt so bad and scared of what was happening to me. Now, they are still there but sometimes worse than others. I have never been treated for anything because as I said before,I haven't been diagnosed yet, still waiting on the results. Some days I hardly notice it and others you can't ignore it. My heart races every morning when I get up around 5 am, then it slows down and then periodicly throughtout the day it will beat faster and then calm down again. Sometimes it so bad in the am that I have to lay back down in bed and calm down before getting ready for work. It is horrible! Anyway, I hope this helps.
Most definatly, thyroid problems are a lifelong struggle, symptoms can fluctuate from day to day in some people and some will have them under control for long periods of time, it all depends on your body. For me I feel ukky most of the time, I have been on medication for over 1-1/2 years, I have better days and worse days, I can usually tell if my TSH is going up, I get more shaky, an over all jitteryness, my heart will beat faster (upwards of 90 beats a minute while resting), I'll get cold easily.
Its a frustrating illness, good luck to you, I hope you feel better soon.