Can an orange pet mate with another orange cat and have a green offspring

Yes. 

This is under the assumption that both orange pets carry a gene for the green colour.

If both orange pets for example have Rr and Rr, where R is the dominant orange colour and r is the recessive green colour
in 1/4, their offspring can be green because their pets would have a genetic probability of:

RR, Rr, Rr, and rr - green. 

The answer would be true