I know someone who is trying to workout throughout the entire day.
10 pushups here, 10 pullups there.

Over the course of an entire day, this will translate to 100's of reps per day.
This is a lot more than you'd ever do in a single traditional workout.

Has there been research on this type of fitness?

All I ever saw was this recent one relating to heart disease and multiple 10 mins workouts
The 10-Minute Workout, Times Three
The 10-Minute Workout, Times Three - NYTimes.com