This character really makes my day! When I see 够 today and just find that its literal structure just helps to make sense of its meaning. Just look at this sentence: 够了，别说了！Enough, don’t say any more!
Actually, 够 is a semantic-phonetic character composed of the phonetic component 句 gōu and the semantic component 多. The original meaning of 句 is “bend.”. 句 has two pronunciations jù and gōu. jù is for the meaning of “sentence” while gōu is for a surname such as the famous historical figure 句践 (replaced by 勾践 later).
The original meaning of 够 was “The load-bearing planks of vehicles/wooden racks begin to bend because of the more-than-enough weight.
The original meaning of 够 was not changed much and all the present meanings are closely related to its original meaning. In modern Chinese, 多 has the following uses.
Verb
1. be enough, for example:
够标准 be up to standard
钱不够花 not have enough money
时间不够 not have enough time
不够资格 be unqualified
2. reach
梯子够不着窗户。 The ladder won’t quite reach the window.
Adverb
enough
今天天气够冷。 It’s pretty cold today.
她哭了个够。 She wept her fill.
说的够多了。 Enough said
Adjective
tired of
天天吃同样的饭，我真吃够了。 I’m tired of having the same kind of food every day.
See also the component 夕
So 句 = 勾?? In your post above, you used them interchangeably (paragraph 2)
No, they can’t be interchangeably used in modern Chinese although they were interchangeably used during some period for certain meanings.