Looking at the stock messaging app, it doesn't look like it. However, Handcent (don't worry, it's free) does do this, if you would be willing to switch apps. (The other major third-party text app may also do this, I honestly don't know.)They both (or any other messaging app, for that matter) access the same messages, so you don't have to import current messages or anything. And if you decide you don't like it, you can go back to stock and have all messages still there.
If you do try Handcent, to get reminders you go to Menu > Settings > Notification settings. Then make sure Notifications is checked, and go into Notification settings. Scrolling down brings you to the Reminders section, where you can enable it and set the number of reminders, the time interval, and if you want the screen on for reminders.