Yes you can but don't.
That TC will want all that space for back ups, so you'll run into problems down the road.
Further... is that a wireless connection? A strong warning: If you're trying to edit the Library (that is, make albums, move photos around, keyword, make books or slideshows etc.) or edit individual photos in it via Wireless be very careful. Dropouts are a common fact of wireless networking, and should one occur while the app is writing to the database then your Library will be damaged. Simply, I would not do this with my Libraries.
You can move the Library to any disk formatted Mac OS Extended (Journaled)
Make sure the drive is formatted Mac OS Extended (Journaled)
1. Quit iPhoto
2. Copy the iPhoto Library from your Pictures Folder to the External Disk.
3. Hold down the option (or alt) key while launching iPhoto. From the resulting menu select 'Choose Library' and navigate to the new location. From that point on this will be the default location of your library.
4. Test the library and when you're sure all is well, trash the one on your internal HD to free up space.
If you are using the Time Capsure with Time Machine then no. Not unless you partition capsure into two partitions: one for iPhoto and one for Time Machine. The partition for the library should be large enough to take in future expansion as more photos are imported. But the both cannot be on the same partition.