No, it is far easier to download an openbsd cd image from canada than it is to physically carry a gun.
Effective like prohibition was? Or the war on drugs? All that will happen is people will stop using macOS and Windows because that is all the US government can pressure.
The effectiveness of limiting proliferation is tied directly to the difficulty and the scarcity of the human capital involved, this is why restricting the proliferation of small arms which can be build by anyone with some machining experience is near impossible, but limiting the proliferation of say nuclear arms and technology is quite possible.
It would surprise me if the NSA (or any other agency) doesn't have a list of all or most software engineers and mathematicians which are capable of designing crypto, that mailing list isn't that big.
People can easily hide data streams inside video-streams/ text-files/images to circumvent trivial screening. The government won't be able to do anything effective without massive costs and draconian measures. Not to mention people outside the US can carry on however they like anyway.
What will happen if say we do wake up to a post quantum world with much of our asymmetric cryptography being worthless. Do you really see people being able to develop a new RSA level family of algorithms at a hackaton?
If you can't increase the work that needed to be done to break your encryption at the same rate as your adversary increases their capabilities you are going to lose and lose badly.
And draconian measures and extreme costs is just what they are proposing, I'm not advocating that it's going to be effective at first or cheap, but dismissing it as even if they want too they will never be able too is just as foolish as voting for Trump ironically to give him a sympathy vote.
Go ask people from East Germany, pre-Glasnost Russia and even some countries that exist today how easy it is going to be to evade surveillance enmass.
You should never be dismissive of threats no matter how far fetched or unlikely they are or how incapable your opponent at executing them might be, this is probably one of the more important lessons one can take from history.