Does 的话 in 这句常挂在嘴边上的话，便点点头答应了 create "If~" subclause? In the following sentence:


  小姐见他有点儿犹豫，便有声有色地向他介绍吸粉的妙处。这时，他想起了，“在社会上混，什么都得尝试尝试” 这句常挂在嘴边上的话，便点点头答应了。


Regarding this usage of 的话, the first I came up with is the use of "If ~, then ..." structure. But this lacks the two fundamental points:


It lacks 如果. But I know it has no problem grammatically, and the omission of 如果 is common.
It lacks 就 in the main clause. If subclause is 如果～的话, then the main clause needs 就, 那, or 那么.


So my questions are:


Is my understanding that the usage of 的话 here is "If ~"?
If it is correct, is it acceptable to use 便 in the main clause instead of 就 or 那?


The sentence also sounds a bit awkward, meaning:


  If this sentence always hangs on the mouse, (he) nodded the head.


Which sounds a bit awkward. "As long/far as" or just use "so" sound more natural for me, like:


  This sentence always hangs on the mouse, so he nodded the head.


So how does 的话 work here and what is the correct meaning of the sentence?
No, it's not a if...then... structure here. 

话 here is used as its literal meaning， words or sentence.

The main clause is actually 他想起了话. And the 话 he recalled was “在社会上混，什么都得尝试尝试”, which always hangs  on his mouth(implying he often says that sentence.)


  他想起了，&lt;“在社会上混，什么都得尝试尝试”> {这句常挂在嘴边上的}话


So when that sentence came into his mind, 便点点头答应了 he nodded and agree to do it.