I've been on Synthroid since I was about 20 years old.
I just turned 40.
I was heavy my entire life. Peaked at... oh, about 318 pounds (just under 5'11" for reference, I was huge). That was maybe a decade ago.
Dropped down to 250-ish, back up to 280-ish, got serious a year ago, and I'm presently 208 pounds. I ride 60-80 miles per week, and I do situps and pushups daily.
Yes, it's possible. Yes, it's hard. I live on chicken, turkey, salad, and lowfat cottage cheese. I don't remember the last time I had anything really carb-y. I miss bread, and pizza, but I simply don't eat that stuff anymore.
I don't think, in my case anyway, my thyroid issues hindered my weight loss. My medicine keeps my levels in the normal range.
Weight loss is hard for everyone, and again, in my opinion, I don't think my hypoactive thyroid hindered my weight loss.