Yes, you can use the portable crib for your newborn. We did the same thing when we had our second child...18 months after our first. We didn't have the room for a second full size crib (only a 2 bedroom home at the time) and our porta crib worked out perfectly! We also got the thicker mattress and it was wonderful. The only thing I noticed, was that as he got older, you can hear his every move. I don't know that you should add two mattresses, just use one of the thicker ones that you can buy to fit.
Also want to add, that my oldest son loved his crib...don't rush him out of there. Your newborn will be perfectly happy in the porta crib for many many months. I think ours was in there for 9 months, and he was very very happy.
Good luck!