Sounds like a good idea but wouldn't work for me. My seedlings can be quite small when I plant them. If the tag was tied to them it would either strangle the fan as it grew or would be too loose & fall off when the plant was dug up.
I'm guessing your seedlings grow much faster than mine so it might not be an issue for you.
I have a few seedlings that have lost tags but since I only plant 20-30 seedlings a year I can typically figure out the cross when they bloom. I have 3 now in a pot & am pretty sure I know the parentage of 2 since there was the only one tet cross. The other crosses were small dips & the fans are huge so I'm going with the tet. If the flowers are red (the tet cross was 2 reds) I'll be positive!