We wrote our own separation agreement, will a notary make it a legal document?

I'm not sure what the law is in TN, but in Maine, just because folks sign a separation agreement doesn't mean that the court will enforce it. And whether or not a notary witnesses it doesn't make any difference. The concern is that the court must be sure that all your issues have been resolved and that you've followed state law. For instance, in Maine there are guidelines for child support. If you decided that you didn't want child support and drafted a separation agreement or settlement agreement with no child support, the court would probably not enforce it. Again, talk to a local lawyer who practices in your area.