unless you order any change to your pitch angle
Almost correct, except you should have written "unless you order any change to your flightpath" as Amadis said. On a Toulouse product in normal law, pulling or pushing on the sidestick commands a change in g-loading, left and right commands a roll rate. So in your example as long as you increase thrust smoothly, at the end you will still find yourself in level flight but at a faster airspeed and a lower pitch angle.
On Seattle products, it's pretty much as you said... I'm not familiar with the T7 but I do believe you trim for a specific speed, and on the 744 -if we ignore the effects of the centre of thrust of the underslung engines not being aligned with the centre of gravity (so a change in thrust requires a change in trim)- it's again pretty much as you said.