I don't completely agree with that, no. The physics are actually fairly complex, however simply showing that it isn't a direct proportionality is relatively straightforward.
For flow out of a rocket, there are really two cases to consider: choked flow, and non-choked flow. Choked flow is when the flow speed reaches mach 1 at the throat of the nozzle, and is generally the case for a gas with a chamber pressure at least twice the ambient pressure surrounding the nozzle (details vary slightly, but I'll ignore that for now). In the case of choked flow, the flow speed is relatively trivial to compute, since it depends only on the gas in the chamber and the temperature in the chamber. Interestingly enough, it does not depend at all on the pressure, so long as the pressure is sufficient to maintain the choked condition. For a rocket without a diverging nozzle section, the flow speed will be mach 1 for all choked conditions. Thus, the momentum of the air leaving the nozzle will indeed be dependent only on the mass flow through the nozzle. Since the mass in the bottle is directly linearly proportional to the initial pressure, this would seem to support your assumption so long as the flow was primarily choked (which is a safe assumption if Pchamber >> Pexternal). However, this is ignoring the fact that there is also a force from the pressure at the nozzle. Since the pressure at the nozzle will be directly proportional to the pressure inside the bottle, the total momentum change to the bottle will be slightly larger than twice as much for twice the initial pressure. I'll also note that this is making a couple of other assumptions - namely that the bottle mass is much larger than the propellant mass (so I can neglect the change in mass throughout the expulsion of the propellant), and that the chamber is isothermal throughout the expulsion of the propellant, which is clearly wrong (but an easy assumption to make). The end result, however, is that the proportionality is clearly not linear, although you could get it fairly close to linear through the use of a very high expansion ratio nozzle (which lowers exit pressure and increases exit velocity) combined with a very low flow rate (to keep the chamber as close to steady-state isothermal as possible). However, this isn't a very realistic case (as it would require either near-vacuum exit conditions, or an incredibly high chamber pressure).
In the situation where the flow is not primarily choked (in other words, Pchamber is not much much larger than Pexternal), it gets even farther from a direct proportionality. This is because in this case, the exit speed depends on the pressure in the chamber, with higher pressure causing (obviously) higher exit speed. It isn't a linear proportionality, but we'll ignore the math for now and just look at it conceptually. If you start with some pressure such that the flow isn't choked, you'll get some total momentum change from it. Now, if you double the pressure (and assume the flow is still not choked), you have twice the mass in the same volume of chamber. The first half of the mass will leave the chamber more quickly than the second half, since the pressure is higher. After the first half has left, then you are left with the starting conditions from before (with half the pressure). However, since the exit velocity (and thus the momentum per unit mass) is higher during this first half, the momentum imparted to the rocket will be more than doubled by doubling the chamber pressure.
(Hopefully this makes sense)(Andrew: your equation isn't quite right... you have to consider both pressure thrust and momentum thrust of a nozzle, thus the thrust coming out of a nozzle is equal to dm/dt*vexhaust + Pexhaust*Aexit)
