Would working in a Veteran's Home count as experience?

I would think so! As hard as VA nurses work!

It depends on what type of VA facility it is. If it's a long-term care facility, your time there would count as LTC experience just the same as if you worked at any other LTC facility. However, if you are looking to travel and work in med/surg or another area, then your LTC experience will not count as "med/surg" experience.