This is a terrible idea. I don't think you could suspend someone's disbelief into thinking this would work even in a fictional world.
If you are vaccinating your people as a whole, the world at large will know you are up to something. Otherwise, your own people are at risk. The enemy can destroy you simply by sending your spies back, plus a few extra infected people of their own.
A nation should always assumed that it is being spied on, as well. If you have a vaccine, so do your enemies.
If you wish to go for biological warfare and you don't want to figuratively shoot yourself on your foot, you don't go for a killer infection that will either be too easy to contain, nor powerful enough that it may come back at you. If this has to be a plot point for you, then the powers that be in your world have thrown reason outta the window anyway.
The situation changes if the enemies are biologically very different from you - such as aliens, or fantasy races.
In Arthur C. Clarke's Rama series of books, a group of humans is at the brink of starting a war against a much more advanced species. The aliens preemptively hit the humans with a disease similar to what you describe. The aliens can cure it, but they don't have to worry about it because it won't affect them. This renders the whole worry about your weapon coming back at you a moot point, thus allowing for its usage without much suspension of disbelief.