Yes and no!
It proccs Ravager, Viper and Selene but it doesn't procc axe bleed or redguard passive.

This thread discusses it more in depth. According to this player channeled attacks (like sweeps/dot) are not considered melee.

While technically mostly true, here´s the lowdown in my experience: The ONLY way to know is to test the specific attack. In general, 'melee' means non-channeled stamina attacks, non-aoe, at close range (including gap closers that do the striking close up), but there is weirdness. I wouldn´t trust number colors or skill descriptions. Just try steel tornado and be surprised...

The game is simply put messed up in this respect and there´s a lot of false information and conjecture out there. Things are not logical (for example cruel flurry doesn´t affect jesus beam which it absolutely should according to the description, while it *does* affect dawnbreaker which according to the tooltip it shouldnt). Jabs is one of those aberrations - it procs plenty of melee direct damage attacks while being extremely similar to flurry which does not proc melee. And no, it is not the burning light passive that triggers the procs when using jabs. To be honest I´m not sure what CP affects jabs since I lost my notes on it, but IIRC (so do not take this as gospel) it increases with thaumaturge with small increases for master-at-arms that Im not sure weren´t just UI errors. Again don´t trust me on this but test it yourself.

You have a build idea; here´s what I do: use foundry tactical combat, spend some money on CP respec (I dont have PTS). Test your build.

Do not trust the UI descriptions. Repeat after me. Do. Not. Trust. Anything. But. What. You. Test. Yourself.