If you keep with the same schedule, i.e. start your first Alesse pack when you would normally have started your next Diane pack, you should be fully protected. You could use a backup method (i.e. condoms) for the first 7 days of your first Alesse pack just to be sure.

You body may need some time to adjust to the new pills, assuming there is any difference in the levels/balance of hormones. So, you may experience some of the side effects that are typical of the first couple months for a new pill user. Your doctor will likely have scheduled a checkup within a few months to make sure you're happy with Alesse.

Personally, I was on Alesse for years, then tried Diane for a few months to see if it would help clear up my skin. It didn't clear up my skin so I was switched back to Alesse and stayed on Alesse for years after that. Both transitions were seamless (didn't change my scheduling) and I didn't experience any side effects as a result of switching.