Ya. Just do it. If folks have a telephone and access to the company's internet and database, there is no need to be at the office. No need to go crazy with planning and special hardware/software.
Just do it. I think your company will be surprised at how easy it is. That day, they will save energy on lighting, electricity, cooling, water, etc. If you do it once per week it could cut your energy costs and cleaning/maintanance costs by as much as 20%.
Don't worry about slackers. Employees who will slack off on "work at home day" are already slacking off at work - only when they do it at work, they are often gabbing with someone else and multiplying the inefficiency.