Yes, you can open the windows or doors in a room with the air purifier. Fresh air is always better for your home. At most, it would bring in some pollen that the air purifier can readily deal with.
However, if you live in an urban area with lots of traffic, the outside air may not be the best. While the air purifier will work, as usual, opening a window would only make its job harder as more pollutants will enter inside the home.
If you happen to have an air cleaner with an air quality analysis feature, you can check to see if opening a window or door reduces the air quality by a margin. In most suburban areas, it should not be an issue having a window or door open with the air purifier running.