Yes but anyone can look at your profile and see your rep was earned via asking instead of answering. Whether SO rep is relevant or not is debatable, but if it is, rep earned by answering is almost certainly more valuable.
I understand where you're coming from - but - I'm of a mixed opinion of whether that's actually true. Asking a lot of questions might be equally valuable if they're questions of increasing complexity, that show growth and development over time.
Back to Malcom Gladwell's "Outliers" (in which he states that the requirement to master anything seems to be 10,000 hours of practise).
With 10,000 'hours of questions', assuming progression and growth, would you not find yourself at the same or similar level of mastery as someone who'd provided 10,000 hours of answers?
Quite frequently nowadays, I find myself at work seeing a question about something not functioning quite right - (height and width of a graph, cross browser/OS page performance & display) and I find that I've got an immediate answer, because I asked the question on stack over the weekend (when I'm doing my fun projects).
Another interesting point - that I've just noticed this morning, is that I think there may be an Algorithm in Stack that "bubbles up" questions about things that you've asked questions about in the past.
My initial attempt to "give back to stack" were met with nowt because I couldn't find any questions on topics that I have relative expertise on - but - now that I've asked a number of questions on the things that apply to me (DOM, jQuery, Ajax, Selenium, PHPUnit etc...) Questions with those tags seem to be closer to the top of my list.
Maybe you've got to ask enough questions for stack to know what questions to ask of you.
It's really neat. I actually quite like it there :)
Depends on what your employer asks for. Some might rather employ somebody who knows how to harvest free labour off the internet, rather than `waste' their time solving other people's problems for free.