In "theory" yes, you could jack the car up while still inside.
I've owned a TR-3B (same frame, same jack hole etc.) since 1968 and have had more than my share of flats by the side of the road and loose exhaust systems that needed an expedient coat hanger repair to get back on the road.
The jack was a nice idea in theory, probably created by a bunch of well meaning design engineers in a nice, warm, dry research & development center with a concrete floor I bet.
It did work, under the right conditions anyway. But you really had to get out and check under the car to be sure you had the jack fully engaged on the little welded on bracket.
But the reality was you needed a pretty good angle to crank the jack and you would have a hard time getting the torque on that ratcheting handle with it held between your knees. Besides, without getting out and blocking the wheels you stand a good chance of it rolling right off the jack when you step out to loosen the wheels. Anyway you have to break the studs loose before you get the wheel off the ground, so no matter how you slice it you're gonna get wet and dirty.
Other obstacles were that the jack was usually in the spare tire hole on a TR-3 and was quickly rusted into being useless by the time you needed it. Remember back then this was everyday transportation for some of us, not a weekend car.
Plus the footprint on that darn jack was about the size of a silver dollar and turning the handle by the side of the road usually meant jacking a nice neat hole in the mud. As a result I carried a piece fo scrap 2 x 6 everywhere I went to put under the jack and another two to block the wheels.
I bought a cheap scissor jack as soon as I could afford it. It's still in the trunk.
My old jack and ratchet handle is now totally refinished and repainted and looks great in a tool kit roll.
(The better, and officially frowned on, use for the hole in the floor was as a traveling rest room. When driving to Northern Wisconsin on fishing trips, my brother and I, with the aid of a piece of radiator hose, could relieve ourselves with out stopping. True Story: Once, outside Rice Lake, we actually had a nice man pull up to us and let us know our radiator seemed to be leaking. Didn't have the heart to say, "Nope, for a change it's actually not the radiator that's my brother leaking.")