No it wont OR Very slight chance are there, What makes Oniks/Yakhont/Brahmos deadly is they are impossible to intercept at low altitude, P-800 is extremely fast 2000-3000km/h giving the defending system like barak8 a min or less from 70kms to get a lock is extremely difficult, The Supersonic missles use speed which reduce reaction time of defending system, to kill it, one must increase engagement range..
The only way is to engage the missile 100km away, Oniks/Yakhont/Brahmos active radar head has a range of 75 km, which means that at this distance from its target it can start pinging it independently (without outside corrections from the launch platform). After it has pinged its target, it dives into the sea-skimming mode.
Which basically means that the only chance you get to intercept Yakhont is outside of the 75 km radius, when it is still flying at high altitude. Or terminally, with a CIWS, but that is of course more of a Hail Mary pass.