If the Warlock is inside, NO. If they are outside, Maybe.

The real key here is the wording on Hunger of Hadar. The spell breaks itself down into being inside the sphere, and being on the outside looking in. We'll use that same breakdown as well.

(emphasis mine)

A 20-foot-radius sphere of blackness and bitter cold appears, centered on a point with range and lasting for the duration. ... No light, magical or otherwise, can illuminate the area, and creatures fully within the area are blinded. - *Hunger of Hadar, Player's Handbook

Inside

If you are fully inside of the sphere you have the blinded condition. Devil's Sight does nothing to counteract that condition.

“A blinded creature can’t see and automatically fails any ability check that requires sight

Outside

This is where the RAW gets fuzzy. As Justin T mentioned,it would be a DM discretion issue on "blackness" being the same as "darkness". Within the text of Hunger of Hadar it mentions opening "a gateway to the dark between the stars". This uses the word dark, so I would probably rule that you can see into it. At the end of the day though, it would be up to your DM.

Blindsight or Tremorsense are the only abilities that let you 'see' through fog or smoke.

I'll spare you my original overly-off-topic explanation; suffice to say that according to the rules of visibility in 5E, when something is blocked by something else, there is nothing anyone can do to see through it except for possess the above abilities. You are 'blinded' by the object that is blocking you, and until that thing that is blocking you is removed, you will always be 'blinded' by it.

Tremorsense and Blindsight are the two things that RAW let you detect the location of things without having to see them, and as such these are the two RAW things that would let you look through heavy smoke. Neither is available as a class ability, so your PCs are not likely to have access to them.

As you mention, Blindsense does not let you see through smoke, because Blindsense only works when the person you're looking for is hidden (took the hide action) or invisible (had invisibility cast on them).

Starting at 14th level, if you are able to hear, you are aware of the location of any hidden or invisible creature within 10 feet of you.

If you're just standing in a fog cloud, then someone with Blindsense cannot detect you any better than someone without Blindsense.

If you're worried about a smoky room, you can look at the spell Fog Cloud to see other ways to get around it, mainly:

[the fog cloud] lasts for the duration or until a wind of moderate or greater speed (at least 10 miles per hour) disperses it.

So, it looks like RAW, mild to moderate winds can disperse fog/smoke to a degree that it stops interfering with vision. In that case, if one of your PCs has a spell that generates wind, then by the Fog Cloud rules they could use it to disperse the smoke and see through it.

They could also have the party barbarian tie large paper fans to his arms and flap them like the dickens, but that may or may not be too silly for your campaign.