yes. Also, yes and no too.
yes d.r. you can put a 3/4" pipe after a 1/2" pipe, and it will help a bit by reducing the friction that slows down the flow of water.
However your 1/2" pipe does have a true physical mechanical maximum flow rate which will prevent multiple jets from getting the optimum or the maximum flow. So no, it is not really advisable by any objective standard to leave a 1/2" in the wall as your supply pipe, not even for a short run. The longer the run, the more the friction which slows down the flow even more.
Somewhere in the basement, where your water supply comes into the house, the pipe is larger than 1/2". Where your pipe gets reduced down to 1/2", is where the greatest "bottleneck" begins and higher friction prevents water from flowing as fast as it will need to if you want multiple multiple jets to work as they might...
When a long length of pipe is made half 1/2" and half 3/4", it produces the same output whether or not the flow is going in one direction or the other; this illustrates the principle that the effect of the reduction is a linear sum. The sum of the reductions, of the 3/4" pipe and the 1/2" pipe. Both have their friction and both reduce flow over the distance. I repeat that having a 3/4" pipe at the tail end is still a good thing just as it would be if you had a longer 3/4" pipe way back before the reduction in size occurs.
Still may not give you the hoped-for result. How many jets? How many might run all simultaneously? How much is house water pressure? How long is the run of 1/2" pipe? I mean from the initial point of reduction up to the point where you are hoping to increase size to 3/4".
david