To clarify, join yes, R2, in your diagram, can have interfaces in both areas 1 and 2, but it would not be an ABR w/o an area zero interface. R2, for any traffic that passes through it, could forward traffic from one area to the other but it would not redistribute area 1's routes to area 2 nor the converse. I.e., in your diagram, R2 would have the complete area topologies for both areas 1 and 2, but R1 would only have area 1's topology, while R3 would only have area 2's topology.
BTW, with only the 3 routers in your diagram, I believe you can make R2 an ABR by simply using a loopback interface, on it, placed into area zero.
PS:
In the above, I'm also assuming you're running OSPF in just one OSPF process, on R2. If you ran each area, on R2, in a separate OSPF process, R2 will still forward traffic, flowing through it, between the two areas, it will also not, by default, share routes between the two areas, but two differences would be, first adding area zero, would not, by default, share routes either (remember, you can now have two area zeros, one per OSPF process), second you can redistribute between the two OSPF processes, which will share routes. The latter would function much like an ABR (although it's still not an ABR), between areas 1 and 2 (BTW, like area zero, you can have both those areas per routing process, for example, rather than areas 1 and 2 you could have two areas 1), but, instead, your router would be an OSPF ASBR.
