We use it successfully in IE here, but what we've found is that you need to make sure your IE isn't running in IE8 compatibility mode. Also, you'll probably want IE10 or preferably IE11 (or Edge) for this. We still struggle with getting the compatibility modes correct, and some things only work when we logon directly to the New UI, but don't work if we logon to the NWBC interface first and then link to the New UI (we're still in a sandbox phase with our own New UI and SRM 7.13 upgrade rollout).
You can check the "browser mode" and "document mode" in IE by hitting F12 on your keyboard while looking at the relevant page.
There is a great blog by Maya Amit at IE and Portal – Standards/Quirks Mode Evolution (or Love-Hate Relationships) which describes the various relationships between browser and document modes and the different web technologies from SAP. It isn't New UI specific, but it does address SAPUI5, which is the underlying technology of the SRM New UI.
Cheers,
Matt