Is it true that people tell the truth when drunk?

People tend to say whatever comes into their head with little processing or filtering. That means they're unlikely to lie, and less likely to lie convincingly, because it takes too much concious mental effort, but that's not quite the same as saying they tell the truth. People often have negative thoughts at a subconscious level, that usually they dismiss on second thought as unfair or irrational. Drunk people lose that ability and the more primal thought processes come to the fore. This is stuff like fear, anger, sexual longing. Alcohol is also a depressant so people can feel more negative than usual when really drunk, as well as losing the ability to reflect on those feelings and the inhibitions on expressing them.

It is different for everyone..Mostly people talk a load of nonsense when drunk.
Many people when drunk make things up to try impressing others but wind up being a fool.

They are less inhibited so will likely speak more freely..

It can be true, so let this serve as a red flag in your relationship.

they cannot control their thoughts when drunk. whatever pops in their mind or whatever runs deeply in their minds, reveals, when drunk.

It is a myth that those who are intoxicated speak the truth. They simply speak without the normal filter. Whatever thoughts, emotions, whatever pops in their heads at the time, come out. It may or may not be truth. They may or may not even believe it at the time. Many think they are clever while intoxicated and try to manipulate at the time. One can't read into, believe, nor judge on what one says while intoxicated. The only message sent is about how they got to that point in the first place .

The effects of alcohol will vary from person to person. It is not a "truth serum"... but in many cases it might make someone open up about themselves, and say more than they otherwise would.
Some people when drunk will decide that it is funny to make up a bunch of lies, just to see other people's reactions.
Some people when drunk will punch your lights out for looking at them the wrong way.
I can confirm that otherwise good people may say horrible things when drunk. Are these the things that they always think, but keep to themselves? Who is to say... On the plus side, horrible people may not be quite so horrible when drunk...
In answer to your question, no, you cannot count on anything that a drunk person says as being the truth. Alcohol can, for example, make two people have sex when the reality is that they don't really like each other very much, but they're desperate and options are scarce.
Alcohol definitely will make a human being act with less caution... but tell the truth always? No way, some people's secrets are so close to their chest that a bottle of whiskey won't get it out of them before they pass out.

They are less inhibited so will likely speak more freely.

A drunk speaks a sober mind.

No. Their judgement is impaired by the alcohol and they say anything that comes into their heads, right, wrong, or total nonsense.

I would be more concerned about his allowing himself to get that drunk and how it affects his personality. What you stated are all red flags that he has a drinking problem and needs some major help.

That is a far larger issue then anything he might have said while he was too plastered to know what he was doing.

If he is unwilling to get help, run - do not walk - as far away from him as you can. Or you can anticipate a lifetime of ab use and misuse from him.