Sharepoint won't work unfortunately, IIS will run, however you can only serve static web pages as ASP.net cannot be installed on Server Core.
More details on this page at Microsoft.
Server core is a great technology for infrastructure rolls however is very limited when it comes to installing applications.
The following taken from the MCTS 70-640 Documentation:
"As an overview; Sever Core supports nine rolls:
- AD DS
- AD LDS
- DHCP Server
- DNS Server
- File Services
- Print Services
- Streaming Media Services
- IIS (Without ASP.net)
It also supports eleven optional features:
- MS Failover Cluster
- Network Load Balancing
- Subsystem for UNIX based applications
- Windows Backup
- Multipath I/O
- Removable Storage Management
- Windows Bitlocker Drive Encryption
- Telnet Client