Brian Michael Bendis approves! Even if calling her Spider-Woman would run afoul of the Sony movie rights for Spider-man, calling her by her real name would likely be enough to keep Marvel from getting into hot water. Drew has plenty of comics fans who would enjoy seeing her on the small screen, and she has both a history of appearing out of costume (like she did in “Wolverine” in the late 80s) and a backstory that includes S.H.I.E.L.D.
Depending on who’s writing her, Drew could be a tad too powerful for the show. The answer to that is simple: just don’t write her that way, and allow her to use more subtle powers like her pheromones instead of her venom blasts and flight. Spiders don’t fly anyway!