I think you can do that, but not with default windows system restore. You may want to take a look at more powerful alternatives such as Rollback Rx and others. That's actually a good idea, I'll try to see if it can be done on an external drive too
If you want to do a full resotre, get something like Acronis TrueImage or Ghost, and make a bootable external USB drive. Then you can boot off that hard drive, create a full image of your computer at any time, and resotore the PC fully. Not that this method is not a "backup" bur rather a disaster recovery option like when a drive fails and your system is totally dead, or if you want to just wipe the system and startr over.
If you want to free up some space, you can reduce the amount of space System Restore takes up, by default it grabs a large %. Same with the Recycle Bin. If you lower that as well, you will get back many extra gig of space. Depending on your drive size of course.