Hi Ktaal,
No, once you get a consistent EASY routine going, you will not be housebound. But in the few weeks it will take to really implement the routine successfully, you may have to be selective in when you do your running around. As she gets bigger she'll lose that need to sleep anytime she's in the car. My DD was like that until recently, and now she can go for long rides without falling asleep, as long as it isn't nap time. So I plan my outings for right after she wakes in the morning or right after a nap. If I must have her sleep in the car or stroller, I choose to do that for her morning nap, because it is generally shorter than her afternoon nap.
EASY doesn't have to limit you at all. Once you have her sleeping in a crib on her own -- at least for the majority of time, and able to self-settle and self-soothe, it won't be the end of the world if you have to give her a nap in the car, because she won't NEED to sleep only in the car. Also, I think EASY makes mobility easier because I can predict when she'll be eating, awake, and sleeping, so I can plan the day better.
But yes, for now, you may choose to sacrifice the errands in order to get her on a consistent routine. Check out the EASY forum for example schedules of babies 4-6 months.
Jana