Weight loss is almost 100% entirely about nutrition. So "with the proper nutrition" yes you can lose weight. You can lose weight with any exercise, no exercise, or heaps of exercise "with the proper nutrition".
As others have stated, abs everyday is a poor idea. Like every muscle they need rest if they're working fully. The reason "you can do your abs every day" came about as a myth is because people don't tax their abs enough, so they're fine to do every day because they're not working hard. But what's the point - if they're not working hard?
Is the running planned for every day too? Especially if you're a beginner, that also should be every second day. It's very high impact and hard on your body and you need to recover. But 1 mile? Why only 1? Do you plan to only ever do 1 mile? Most people pick up a couch to 5k type of programme and aim for 3 miles. If 1 is all you can do, mix running with walking.
Effective cardio (especially for weight loss) should be 30-60 minutes. It's VERY unlikely your 1 mile will take that long.
So ... proper nutrition and: alternating a half hour run/walk with a full body strength routine so you do one or the other daily (1 day a week 'rest'). That's a good routine! :)
Deb, in New Zealand