It is possible. In a customer network we are doing IPSec over GRE and running EIGRP. I have configured IPSec for both tunnel mode and for transport mode. Both of them worked.
we have about 50 Companies in the whole world connected via GRE over IPSec. A lot of the companies are meshed. So EIGRP can find the best way to the HQ in DE if we have Problems with the ISP. Additional we can use floating static routes to enable ISDN-Backup when Internet is down. It works fine.
The real question is not whether you are connected using a single physical interface at the central site. I have a customer who is currently using a single physical interface for about 90 GRE tunnels with no issue about split horizon. But these are traditional point to point GRE tunnels. If you connect to multiple remote locations with a multipoint GRE tunnel then there is an issue with EIGRP split horizon and you would need to turn off split horizon. If you do not disable split horizon the symptom is likely to be that all remotes can talk to the central site, the central site can talk to all remotes, but one remote will not be able to talk to other remotes.
No, we don't have a Problem with splithorizion because we have for each Company a own GRE-Tunnel (point-to-point) for the Routing-Protocol it's like a own Interface for each Branch. We don't use Multipoint GRE
