Nice gift! I can't tell from that angle, so far away. Maybe a 'duckfoot' type if I'm remembering the right word.
Yes, any Coleus piece will do its' best to grow roots, rarely fails. With plants that wilt so easily like this one, I like to hold them in water for a few days to a week, until I notice tiny roots starting to form. That gives me the best results, though others might have another method they prefer, and I've certainly grown plants from pieces just snapped off and plunged into the ground or a pot.
Yours reminds me of the one in front in this pic, but I don't remember its' name. These are cuttings brought inside to save over winter.
I have no idea how big Coleus can get if it has more time, but it was a good year for them last year, these pics are from late October.
That's a 55-gallon barrel to the left, not all Coleus.
Growing in used-to-be washtubs (bottoms rusted/gone.)