"In the example above, I am not sure if the word is necessary." – Have no doubts, it is indeed necessary.
"I would think that people reading this description would understand that the things stated are not intended to be read as fact." – No, not at all.
"Does “supposedly” have a negative connotation?" – No, not by itself. It is the context that may give the color of negativity to it.
a qi gong master supposedly directs the flow of qi
A disassertive marker: Here, supposedly because one is told so, with there being nothing tangible to show that, to make any categorical statement that it does.
supposedly: according to what is generally assumed or believed (often used to indicate that the speaker doubts the truth of the statement).
… New Portable Battery Pack Supposedly Has 22,400 mAh Of Juice, …
Exercising supposedly reduces the risk of cancer.
This does not repudiate the claim of 22,400 mAh energy inside the battery or the efficacy of exercise in cancer cure. It merely adds the proviso that it is someone else's unverified (by the author) claim.
A Supposedly Fun Thing I'll Never Do Again: Essays and Arguments (David Foster Wallace)
The author doubts the claim that the thing is any fun at all. A measure of sarcasm, and clearly, negative connotation, is apparent.
Same goes with A Wholistic Aid for the Supposedly "incurables" (John Raymond Christopher)
The program is supposedly now able to deal with newer terrors like spyware and keystroke-logging programs, ... However, the user is reliant on definitions being up to date – but our tests were none too ressuring on this point.