Using nuclear power, for any reason whatsoever, is looked upon with great suspicion by the existing nations with nuclear capabilities. There are a lot of countries, including the US, that are skeptical of Iran's nuclear program, that they are currently just building reactors, not bombs.
Project Orion included nuclear pulse units that are in practice small nuclear warheads. Also, this combined with orbital capability, would mean a potential for building ICBMs with nuclear warheads.
Even if you circumnavigate the test ban treaty, the international agreements on not spreading nuclear warheads will apply.
However, several countries have not signed the Comprehensive Test Ban Treaty, of them the nuclear powers Pakistan, India, North Korea and Israel. They have instead signed the Limited Test Ban Treaty. On the other hand countries like France and China have signed the Comprehensive Test Ban Treaty, but not the Limited version.
An example of a country not signing any of them is Saudi Arabia.