You're almost on the nose! This is a construction we use frequently, and while related to できるだけ through the use of だけ, it carries a slightly different meaning due to the use of the plain conjugation (連体形) as opposed to the potential form (可能形).
Take these two examples:
1) 飲めるだけ飲んでみます。
and
2) 飲むだけ飲んでみます。
In 1), the speaker is using だけ exactly how you referenced in the second half of your question.
飲める(だけ) → (All/To the extent/As much as) one can drink
飲んでみます → One will try drinking
So in English, we would translate this to something like:
I'll try drinking as much as I can.
However in 2), the speaker isn't talking about their potential to drink anything; they didn't use the potential form.
If we wanted to analyze this sentence like we did 1), we could say:
飲む(だけ) → (All/To the extent/As much as) one (will) drink
飲んでみます → One will try drinking
So literally:
I'll try drinking as much as I'll drink
It doesn't really sound like the speaker wants to drink anything, does it?
If we wanted a more natural-sounding translation, we could say something like:
I'll give drinking it a shot (but don't expect me to drink all of it)
This to me is the key to understanding 連体形+だけ vs 可能形+だけ.
With the potential form, we're saying we'll do all we can, but with the plain form, we're only saying we'll do what we will do.
Applying this to your example, you give:
不満を吐き出すだけ吐き出せば、スッキリするだろう。
If we instead said:
不満を吐き出せるだけ吐き出せば、スッキリするだろう。
This would carry the meaning:
If they get all of their complaints out, they surely will feel better
However in the plain form, as is, I would translate it closer to:
If they (would) just get their complaints out a little, they'd probably feel better
The "just" and "a little" here are my attempts to show that "they" are probably a bit reluctant to complain.