Yes they can have different kinds. I am a bit newer to guinea pigs so didn't know that at first and was only using timothy. I did switch to orchard and love it. Sometimes I still use timothy when I forget and have to run to the store. I have to order the other kinds online.I have hay all over my house thanks to the house bunny. I don't give it any to the rats though. For similar reasons as moon, messy..the last thing I want is more hay around haha. I don't know about gps, but can they have different hays Moon? I only do timothy once in a while because of allergies. Orchard doesn't seem to give me the same issue, so I get more of it.
What is the difference between 3rd cut and 2nd cut hay?If you do get some sort of hay, I'd highly recommend 3rd cut timothy, orchard grass, or bluegrass. They are far softer than most other varieties and held reduce the risk of them poking their eyes out. (I'd use them myself if my guinea pigs didn't prefer 2nd cut timothy. *sigh*)
I'd just be careful about leaving them alone with it. Maybe just provide some during lap-time? That way you can keep an eye on your ratties.