iPhoto should continue to work just fine, because it will still be on your HD, just in Dropbox's "Watched Folder"
However, from a back up point of view, the jury is still out. One or two people have tried restoring from Dropbox, or moving it to a new machine via Dropbox and found issues, possibly related to the format of the server that it's uploaded to on Dropbox.
One thing I'm not sure about: will changes to the Library trigger an upload of the entire library, rather than just the increments? I doubt very much that Dropbox understands the innards of an iPhoto Library and that could lead to database corruption of the back up.
As a general comment: iPhoto Libraries are huge, and grow very quickly. Unless you have a beast of an Internet connection I'm not sure that the cloud is ready for backing up libraries. We've seen complaints on here from folks waiting days to restore from services like Crashplan etc. How long would 100 gigs of data take to download for you?
Yes, Time Machine will keep a rolling back up on an external disk.
Most Simple Back Up
Drag the iPhoto Library from your Pictures Folder to another Disk. This will make a copy on that disk.
Slightly more complex:
Use an app that will do incremental back ups. This is a very good way to work. The first time you run the back up the app will make a complete copy of the Library. Thereafter it will update the back up with the changes you have made. That makes subsequent back ups much faster. Many of these apps also have scheduling capabilities: So set it up and it will do the back up automatically. Examples of such apps: Chronosync or DejaVu . But are many others. Search on MacUpdate
My Back up routine
My Library lives on my iMac. It’s Backed up to two external hard disks every day. These disks are permanently attached to the iMac. These back ups run automatically. One is done by Time Machine, one is a bootable back up done by SuperDuper
It’s also backed up to a portable hard disk when ever new photos are added. This hard disk lives in my car. For security, this disk is password protected.
I have a second off-site back up at a relative’s house across town. That’s updated every 3 or 4 months.
My Photos are backed up online. There are many options: Flickr, Picasa, SmugMug etc. However, check the terms of your account carefully. While most sites have free uploading, you will often find that these uploads are limited in terms of the file size or the bandwidth you can use per month. For access that allows you to upload full size pics with no restrictions you may need to pay.
Every couple of months I test the back ups to make sure they are working correctly. It’s very easy to mis-configure a back up application, and the only way to protect against that is to do a trial restore.