Charles, that is what Boolean does. You subtract a solid of the cavity from the overall solid.
Not really worth it wil the simple tee in your example but a very good and efficient way when dealing with parts that have complex cavities. The other big bonus is the fact that having modeled the void as a separtate item you can also use that to produce the core box cavities with just a couphe of clicks rather than having to sketch and cut all the shapes a second time. Add to that Parametrics and any change you make to the cavity will automatically carry over to the part and core box files.
Take this replacement cylinder casting for an old gardner engine.

Quire complex cores needed when you see it in section, one for the water jacket, one for the exhaust passage and one for the actual cylinder bore and it’s passage to the hot tube.
All three were modeled and then removed from the overall pattern using Boolean subtract to get the finished casting below

I then used the same three models to produce the core boxes, this is half the water jacket box

And a test of what the core from it would look like again done with boolean

And a test fit of the core in drag again no need to draw things again just use boolean

All three were modeled