Is there a reliable way to check if an idiom (成语) is widely used?
This is by no means scientific but its a fairly good metric to tell you how common a word is:

Search Engine Results Hits. 



Let's take a well known idiom first and see what kind of numbers we get:


本末倒置


Google hits:


  3,030,000 results


Baidu hits:


  19,200,000个


Here's another one:


鸡飞狗跳


Google hits:


  23,900,000 results


Baidu hits:


  17,100,000个


So well known idioms would give us results in the millions and even in the tens of millions.



Now lets take a look at the word in question: 


完事大吉


Google hits:


  110,000 results


Baidu hits:


  986,000个


Clearly it's not a widely used as the aforementioned idioms. 



Next let's look at:

News Results Hits.

News is current and it can give us a closer look at what words are still in use and how they are used.


本末倒置


Google news:


  47,300 results


Baidu news:


  47,300 results



鸡飞狗跳


Google news:


  121,000 results


Baidu news:


  82,700篇



完事大吉


Google news:


  1,110 results


Baidu news:


  26,300篇




完事大吉 doesn't seem to be that common but there are plenty of news organizations that apply this term in their publications. Here are some excerpts from over the past few weeks:


  办理几个案件就完事大吉





  删除APP”就完事大吉了





  有了成绩就完事大吉了


Another thing to look at is 完事大吉 is basically a combination of two words you already know: 完事 (finish) and 大吉 (great fortune). It probably won't take a great effort to remember this idiom and who knows maybe you'll know it the next time you run across it.