"See your ancestor's signature on the day he signed up."
Maybe it is just me, but when I see the phrase "he signed up," I think enlisted and actually joined. While the men did sign their draft card, they were actually registering for the draft. This is why it is called a draft registration.
I realize it may be a little picky and that marketing is not always concerned about the details.
Genealogy usually is.
Words carry suggestions and bring assumptions with them. Those suggestions and assumptions can create confusion later.
So if Ancestry.com wants to use "signed up" in their advertising, I guess that's ok.
But I'd recommend that you reserve the use "signing up" for those who served. Registering is different.
This is why I don't work in marketing.
