Does this seem like a viable approach?

Sometimes I'll sit next to this girl in one of my lecture classes. I've made small talk and got her name, but it's a big class (still have anxiety of approaching in front of other people) and we're watching films half the time (no time to talk).

I was thinking during one of our films pass her my phone which says something like, "Lunch sometime?" And if she looks and nods or something I'll pass my phone back with "New Contact" page.

Seem like a fine approach?