You can manually enter your rides, you just can’t be eligible for the grand prize if I read the rules correctly. Below is what the FAQ Says:

On any given day of the Tour, get out and ride! Make sure to log your workout including your distance, pace and time. You must manually enter your ride data at MapMyRIDE.com/TDF on the Log a Workout page or use the iMapMyRIDE App or other compatible GPS device to record and upload your “verified” ride data. Just make sure your ride data is entered into our systems by midnight EDT.
The participant who submits the best “verified” ride will be awarded that Stage’s winner jersey. An overall leader’s yellow jersey will also be awarded after each Stage. Here are the different ways to submit your ride data:
Upload your ride data effortlessly from an iMapMyRIDE App
Download and use the iPhone, Blackberry, or Android iMapMyRIDE App. iMapMyRIDE app uses the built-in GPS on your smartphone to track your route, distance, pace and calories burned. And it will effortlessly upload all of your ride data to MapMyRIDE.com. Ride data submitted via this method is considered “verified”.
Import your ride data from a GPS device
If you have a compatible GPS device, you can easily submit your ride data at MapMyRIDE.com via the Import Workout from Device option on the upper right hand corner of the Log a Workout screen. MapMyRIDE supports many popular GPS devices including Polar and Garmin. Rides submitted via this method are also considered “verified”.
Enter your ride data manually
Use MapMyRIDE.com to manually submit your ride data. Map out your ride and then log your workout. Be sure to add your distance and time in order to receive your virtual time. Ride data submitted manually is not “verified.” You will still receive your Stage results and be entered into that Stage’s random prize drawing, but you will not be eligible for the daily jersey competition.

For more information on ride data submission and support visit our FAQ page.