It's never that simple. First of all, the currency supply is kind of a red herring. What really matters here is the relation:
Real GDP = Nominal GDP * Price level
So if you care about growth in Real GDP (ostensibly because you consider Real GDP to be a proxy for Living Standards, and that's what really should matter), then obviously the right hand side of the equation must somehow move accordingly. But: that's not the only constraint on what can happen.
Not all trajectories of the variables in this equation are equally plausible, even when they all satisfy the equation.
I read your statement as an implicit one-directional causality. Let me rephrase your statement with the goal of clarifying what we're talking about (and please correct me if I mis-interpreted): if the economy grows (Real GDP is growing), and then nominal GDP is somehow forced to remain constant, then that will cause prices to go down.
But why would it? The main direct driver of real growth is demand. Having more customers is what ultimately causes firms to produce more, build new factories, hire employees. Somewhat more indirectly, the belief of being able to get more customers in the future also causes firms to produce more, build new factories, hire employees.
Now if you force nominal GDP to remain constant, then the first signal that firms receive is that demand stops growing. Hence the first signal that firms receive will most likely cause them to stop increasing production.
Granted, it is conceivable that firms interpret the signal of flat demand differently, and that they react by reducing their prices. This is an empirical question, which seems to be answered mostly in the direction that prices are "sticky".
So in summary, if you force Nominal GDP to remain constant, you will most likely stop the economy from growing.
Note that the reverse of your implied causality is more plausible in a limited sense: if for some reason prices decrease, then this could well cause Real GDP to grow while Nominal GDP remains constant (this is true as long as wages do not decrease along with prices, because then nominal demand can remain the same, while more goods are moved for the same nominal demand). But then you somehow have to explain how that decrease in prices is caused.