I made rice pudding all the time with Minute Rice (like Silversage, I'm assuming that's what your Easy Cook is) many eons ago, as did my mom and grandma. Turned out just fine.
I must confess to never having made a rice pudding, but my mother, MiL and wife all used a short grain rice for puddings.
The term 'Easy cook' rice amuses me. I mean, cooking rice isn't exactly hard. I expect it really means 'quick cook', but again, I've never found it to be much faster than ordinary rice.