Is it possible someone in my office is on illegal drugs  while
exhibiting the following combination of behaviours?

She is always highly stimulated, yet mostly in control. She says she has ADD and
takes meds for it.  She visits the bathroom alot and I hear her
blowing her nose often. She has lost a great deal of weight in the
past 9 months yet she eats a tremendous amount of food. She says she
has a thyroid condition and take meds for it (maybe the dose is
wrong?)

Conservastively she eats 8,000 calories a day. She is 36, 5'11", 115 pounds.
She eats constantly - all day. She does not exercise. She only eats
junk food - candy sodas, desserts, etc.

She has spots on her face and legs that she tries to cover. They come and go. 

Wouldn't drugs like coke and meth (which could account for her behavior) also
kill her appetite?

Sure it's possible. It's more possible you have your nose where it doesn't belong.

Many situations, including medical and psychological conditions may
cause the observables you describe, not necessarily drug abuse.

The only thing that sounds like cocaine or meth use is the weight
loss, however the thyroid affects weight, and medication for an
underactive thyroid would indeed cause weight loss. The thyroid
affects metabolism, the rate at which we burn energy, so that would
also explain why she can eat all day. And if you are eating all day, I
would say that frequent bathroom use would be necessary.

If you think she's using at work, blowing of the nose has nothing to
do with it. You only get a stuffy nose when the cocaine is GONE. Meth
is *usually* smoked so that would not give you a stuffy nose, only
snorting cocaine all night, then stopping when you go to work would
cause a stuffy nose all day. If she's snorting meth, she'll soon need
nasal surgery, it burns holes through the connective tissue in your
nose. But again, she's not doing trhat because it's impossible to
maintain any semblance of a normal life if you are a daily meth user.
Plus, she would never sleep if --because of the stuffy nose in the
DAY, she'd have to be using at NIGHT.

Plus, you didn't say a word about the quality and quantity of her
work, so I assume it's satisfactory. You also didn't mention any other
symptoms that would normally be present in a daily drug user.

I'd say no, she's not using drugs at work.

Prssurcookr may have a point, but on the other hand, persons with a
serious problem need help, and a fellow employee may be in a position
to observe them better than someone (or no one) who sees them the rest
of the time  (this from a parent of a child who once had an eating
disorder).

If Michael is right on his estimates of caloric intake and weight,
something is wrong.  Bulimia (binge eating and induced vomiting) comes
to mind:
http://psychcentral.com/disorders/sx3.htm

I have no idea if that would account for the spots.

I hope one of the medical savvy Researchers looks at this.

I am amazed that anyone who thinks that someone who sees this woman
only at work can have any sort of insight into her life.

Honestly, my eating habits at work are horrific.  Sugary foods,
coffee, tea or soda...but that's what's convenient to eat at my desk. 
I'm constantly in the bathroom because my blood pressure meds also
contain diuretics and I blow my nose continually because the idiot in
the next cube bathes in perfume and it irritates my sinuses. 
Obviously, that means I'm doing meth.

I've dropped a ton of weight in the past year in spite of poor eating
habits at work, but clearly, it must be because I'm on drugs, not
because I dance for an hour every day at home, take classes twice a
week and eat sensibly when not at work.

Be careful how far you jump to reach your conclusions.

For goodness' sake, as the mother and former employee of serious drug
users, whose habits included marijuana, cocaine and possibly meth, I'd
say back off and take a breath. The scenarios and symptoms you
describe might posssibly be suspect, but in the absence of other
indicators do NOT absolutely make a case for any kind of drug use. My
former boss used to leave half-smoked roaches on the sink, powdered
bits of mirror with or without razor blades on various surfaces, get
the "munchies" during all-night work sessions, and betray much more
than a runny nose on days after. My son had pot seeds in his closet,
and a bank bag full of pipes and other drug paraphernalia, left in
open view. To be blunt: you flat-out don't have enough evidence to
amount to diddly-squat. Either spend years in observation (as I did)
or just myob, unless it's having a serious impact on your own work.
And in the latter case, plan to spend significant time documenting
what amounts to self-destruction on the amount of your co-worker, or
become a friend and act as a friend on what you learn. In lieu of
those, and in summation, myob.

Regards,
Byrd-ga

Express your concerns to her supervisor.  You have no right to
intervene except as her friend.  That is about all you can do.  Be a
good friend to her and be there *if* she asks for help.

If her behaviour impacts your work, then you should also report that
to your supervisor.

IMHO, telling your coworker's supervisor your suppositions is what I
most definitely would *discourage* you to do -- you risk to put her
and ultimately yourself in big trouble, specially because the
indicators you mentioned seem much more likely to be due to a variety
of other reasons rather than drug abuse.