Yes that's the bare die.
No, you won't get better performance with paste, at least not without modding the heatsink or using. Those posts, which are there to lift the heatsink so it doesn't hit the transformer IC, means there is a gap too large to bridge effectively with paste.
You could make direct contact if you used a an aluminum orcopper shim to fill most of the gap, which would significantly reduce thermal resistance when used with paste...but I wouldn't bother unless you have good reason to suspect there are thermal issues.
...rightful liberty is unobstructed action according to our will within limits drawn around us by the equal rights of others. I do not add 'within the limits of the law,' because law is often but the tyrant's will, and always so when it violates the right of an individual. -- Thomas Jefferson