Hi,
Yes, the Makefile looks like it can be built with VisualGDB. Simply install our ARM toolchain, add it to PATH and replace arm-none-eabi- with arm-eabi- in your Makefile so that it matches the arm-eabi-gcc.exe executable. However if the project is made to be built on Linux, it might rely on other Linux tools and simply not build under Windows. In that case we would suggest getting a Linux cross-toolchain, getting it to build on a Linux VM and then importing it into Visual Studio as described in this tutorial.
Either way, VisualGDB is flexible enough to build/debug any project that can be built using command-line tools, so you should be able to develop it with Visual Studio and VisualGDB even if it needs to be built remotely under Linux. If you encounter strange error messages, feel free to post them here so that we could try to help you.