Is it possible to build and scale a startup with only remote employees?

It would save considerable overhead expenses on things like rent and health insurance in some cases (for those employees who are in other countries).

What about VCs? Would they look upon such a startup negatively and tend not to fund such startups?

I think it can be done and I am about to do a 6 month test on a new start up I am getting involved with as their Marketing, Sales and investor connector.

It all depends on the skillsets you are bringing together. No reason why software development can be in a different location from business development etc. Modern tools like Skype , email , conf calls etc all make it much easier to do and sometimes having teams in different locations adds credibility and reach.

While "Is it possible" doesn't equate to "Is this the best option for my company", the answer to your stated question is a definite yes. All I have to do to prove that is point out at least one company that does that, and the one I'm going to use is the very successful 37signals/Basecamp. The ability to work remotely is a huge part of their culture, and virtually everybody does it all the time. They even wrote a book about it. I've never read that book, but one of their other books, REWORK is one of the best books I've ever read on business.

Working remotely definitely has its own set of challenges. In a company of 1 or 2 (as founders) you can usually manage things just fine. You usually know each other pretty well, you're both highly motivated to make the company a success, and so on. As you grow, you'll face all sorts of challenges, such as people who just have too many distractions at home. (Some people have a lot going on in their house, and actually get more done if they can get away from it. You may have to arrange co-working spaces for people, or rent out private offices in an office building somewhere.) I'd suggest spending a lot of time reading up on these challenges and different ways that you might overcome them. You'll want solutions that fit with your company's unique culture and problem set, not just ripping off Company X's ideas.

As far as VCs go, I'm not sure I can give much advice. Nothing official anyway. VCs aren't my cup of tea.

But VCs are as varied and different as companies themselves. I'm certain you'll find some that feel strongly you should be physically together, at least while you build the company. But I think that you'll likely also find others that will treat working remotely as a point in your favor, especially if you can articulate the problems you think you'll face (or are already facing) and how you will (or are) solving them. After all, if a company is built around remote work, you don't have to convince people to move to your location (which turns out to be a really hard thing sometimes) and you can draw from a much broader talent pool beyond just the local one.