Please find attached detailed diagram and question.
Can someone explain why "R2" would see the aforementioned route 10.2.0.0?
If the 'noexport' option is on, and R2 is on a different AS, I thought that only R1 could see such route 10.2.0.0. How can the route get propagated to the neighbor AS R2 is in?
Note that the network 10.2.0.0/16 has the NO-EXPORT community set only when advertised to the R2. In other words, in R1's BGP database, the network 10.2.0.0/16 does not have any community so its propagation is not limited. The NO-EXPORT community attribute will be added to it only when advertising that network to R2 but again, it will not be stored in R1's database. An outgoing route-map modifies BGP attributes on the fly but it does not modify the actual BGP database on the router - it modifies only the advertisements. Of course, if R2 accepts this community then it will not propagate the network to another AS, exactly as NO-EXPORT suggests.
I hope this clarifies things a bit.