"new Microsoft tablet"? Is that the $500 Surface Windows RT or the $900 Surface Windows 8 Pro? In the Surface Windows RT (ARM processor) case you have to first figure out how to install Java programs on it. In the Surface Windows 8 Pro (Intel processor) case it would probably work because it runs a version of Windows 8.
A search of the Surface website turned up nothing about Java on Surface Windows RT (or Surface Windows 8 Pro, for that matter).
If you wan to run Arduino you might want to spend the extra $400 for the 8 Pro.
You might be able to use this website for doing test compiles from any tablet with a browser:http://www.arduinodev.com/software/builder/