This winter yes, I usually cycle to the office in work clothes, which for me are slacks, button down shirt and running shoes. I do keep a pair of dress shoes at work. The commute is 7.8 miles each way, including parking lots, when I take the Greenway as I usually do. I'm using a fixed gear road bike with a chain cover, & fenders, which helps immensely because I don't have to worry about oil stains or torn cuffs.
The issue is when it rains, or it has rained and there's mud and water everywhere, and I'll then switch to biking clothes and change at work. I'm fortunate to have access to a fitness center and showers if I need it, though I usually don't. That will change after it warms up and I'll be wearing jerseys, shorts etc on a regular road bike and change or shower every day.