The White Tower has always had a good relationship with Andor so Elayne could easily spin that she did this in the interest of her countrys' nation security and moreover, she was not involved with the construction so she has violated no Oaths; the issue really seems to be that the knowledge of the technology will spread to other nations that might be threats to the Tower, but even then, having a strong ally that is not being forced into an untenable defensive position is worse for the Tower because it essentially means being a leader of a strong country and an ally of the Tower are mutually exclusive.

But, as history has shown, other Aes Sedai Queens have engaged in wars and used the One Power in battle while the Tower wasn't actively involved or in approval.