I do not think the Razer Core will work through an adapter as it connects through a Thunderbolt 3 port, not just a USB-C port. The Surface Book's ports are USB 3.0 and do not support the Thunderbolt 3 connection. An adapter would not change that, and even if it did, would not provide sufficient throughput for data transfer for the Core.
Thunderbolt 3 utilizes the USB-C port, but is a different specification that offers greater throughput for data (40Gbps). A standard USB 3.0 port (regardless of USB-C or USB-A) offers 5Gbps throughput. USB-C itself is only a physical port type and does not determine the speed or protocols for the connection. USB-C can support the USB 3.0 protocol (offering 5Gbit/s throughput), USB 3.1 (offering 10 Gbps), and Thunderbolt 3 (40Gbps), depending on the hardware support behind the actual port. For example, the Yoga 900 has a USB-C port, but it only utilizes the USB 3.0 protocol, so it does not offer the specifications needed for utilization as a power port, nor does it offer the transfer speeds of Thunderbolt 3; you can still plug in any USB-C product and have it connect at USB 3.0 speeds. The Razer Core would not likely work with that laptop either. Many new devices (Dell XPS 13 [new version 2015], Razer Blade Stealth) now utilize the USB-C port with USB 3.1 and Thunderbolt 3 support to make the most of the port, but some do not (Yoga 900). The Core likely only works with Thunderbolt 3 supported USB-C ports, and even then, requires the hardware developer for the laptop to support the plug-and-play requirements to properly run it.
As they have not yet released the Razer Core, they may change how it works, but the USB 3.0 specification at 5Gbps is likely far too little to run an external graphics card and transfer data adequately.