It's very important that the organization is well equipped to handle remote workers (i.e. more than just one or two people are remote). The local people in the company should take pains to make sure that the remote people are included.
As a remote person, it's important to make sure that you communicate often. Deliver well, talk to people, make yourself visible by being a part of things that matter. Look for ways in which things could be better, because they always exist.
Make sure your manager knows your career aspirations, and let them help you with that.
Do spend time in the office and with your coworkers when you get a chance. I've made 4-6 trips per year over the past 9 years. Face time does matter, so take advantage of it!
At many (most) companies, there is a ceiling for remote workers. If you want to be a VP, you'll almost certainly need to be at headquarters. I have had engineering, management, product management, project management, and architecture roles remotely, though, so there is a lot of possibility available!