I'm a big proponent of listening to what your body tells you. Everyone's capacity for the amount of work they're able to do differs so while you may be able to grease the groove for a week with pullups, someone else might not. Why not give it a try for a week and see how it works? I think the two telling factors that will help you determine whether you should keep greasing the groove or not are 1) elbow or shoulder pain, and 2) your times on day 1 and day 3.
Pullups can be hard on your joints, especially if you're a big guy and you're just starting out. If you overdo the pullups by doing them through out the day and then again during a workout, you might start to develop tendonitis from repeated strain and not allowing adequate recovery time (that's what happened to me).
Second, if you start to notice your times on day one and three starting to slip then greasing the groove isn't helping - obviously
or you should switch the days that you're doing it.
Why not try greasing the groove for a week on the same days as your workouts. This will still allow you to recover on your off days. If you notice your workout times increasing because you're muscles have already been taxed by the pullups done through out the day or any elbow pain, then take a week off from GtG and the next week try greasing the groove on alternate days from your workout.
Another idea, might be to GtG with a related exercise to what you're trying to strengthen. So in the case of pullups do towel rows or inverted rows through out the day. The rows will indirectly help your pullups but help avoid strain from the same repetitive movement and also leave you enough energy to perform your regular workout.