You can, but there is no way to get the data out, since it produces the output by attaching it's HTML to the output of the controller (which isn't there on an ajax call).
We're looking into a different solution for 2.0, but we haven't decided on a design yet. One of the options is using websockets, so you can open a second window and view the profiler output in realtime. But that might be difficult or time consuming to make.
Hey, it looks I'm going back to my old way of doing this kind of things: registering some timestamps during the execution, then login them before exiting the controller...