No No.
Firstly, Babur can be deployed for both strategic & conventional role.
In fact there are two version of it, one which is well known is nuclear capable and other is for specific conventional role. It is meant to penetrate in Indian ballistic defense systems as well as air defense in order to render them use less against of ballistic missiles or air crafts.
This missile was particularly developed by keeping it's usage as SEAD asset.....
And yes, it can house conventional war head as well as anti radar seeker.
As far as point of nuclear retaliation by observing "possible nuclear capable missile approach" is concerned, well that is very different thing. Cruise missiles have varying ballistic paths and remote trajectories. By judging trajectory, flight path, possible target it's pretty easy to assume that what type of warhead missile is carrying .
And no one neither respond aggressively by "suspecting" a nuclear capable missile launch nor the enemy fires a lone less leathel sub sonic cruise missile to start a nuclear war