I'm a little confused - are you asking if you can expect to drop 20 lbs in a month by taking Alli and exercising - if you are I believe the answer is yes.
You also mentioned that most of the problem is lack of exercise. I would think that is probably not the case - I would think that the problem is, is that you are taking in too many calories. You can't out exercise (or use Alli) to combat too many calories coming into your body.
I think your best approach may be to realize that you can't have it both ways - eating the high calorie/high quantity foods AND expecting to be thin, fit and healthy.
It's the food. That will have to be curtailed, kept in check. Come up with a sensible eating program full of delicious, healthy lower calorie foods. Stick to a calorie budget. Map out your food in advance and stick to that sucker like glue. Failing to plan is planning to fail.
The good thing is, is that good eating begets more good eating. So once you get going (and that's the hardest part - starting) and get used to this healthy lifestyle, it gets much easier.
So I say, commit to eating very well, making good choices at every turn. Forget the gym for now. Start walking, buy an inexpensive resistance band and get yourself going. Because again, once you get going, you'll see that eating well and exercise is nothing to fear. You will feel great and the results will transform your life.