I saw that method tested along with several others for snake bites and it was a major fail. The conclusion was that it could very well be worse using that method. Suction was a giant fail too and that's the method pretty much considered the only one that works but it doesn't.
Yes. I remember when even the boy scouts taught to cut an X on the skin and suck out the poison. Then somebody came out with a kit that included a suction cup to facilitate sucking the poison out.
Modern science says no. Bring em in, and let the medical peeps take care of it.