Hi,
To answer the question posed in the subject line of the original post to this topic, the answer should almost always be no.
I am a man, and if I had a girlfriend|fiancée|wife|mistress and I asked her if she needed anything when I was running errands, I would be meaning something more along the lines of food, drink, things in general. Going shopping for tampons, make-up, and girly magazines, though, isn't my thing. I think these sorts of things are the things women should get on their own unless they are seriously incapacitated.