Embeddings vs text cleaning (NLP)
I post this here just to summarise the comments in a longer form and give you a bit more commentary. No sure it will answer your question. If anything, it should show you why you should reconsider it.
Points about your question
Before I talk about your question, let me point a few things about your approaches. Word embeddings are essentially mathematical representations of meaning based on word distribution. They are the epitome of the phrase "You shall know a word by the company it keeps". In this sense, you will need very regular misspellings in order to get something useful out of a vector space approach. Something that could work out, for example, is US vs. UK spelling or shorthands like w8 vs. full forms like wait. 
Another point I want to make clear (or perhaps you should do that) is that you are not looking to build a machine learning model here. You could consider the word embeddings that you could generate, a sort of a machine learning model but it's not. It's just a way of representing words with numbers.
You already have the answer to your question
You yourself have pointed out that using hunspell introduces new mistakes. It will be no doubt also the case with your other approach. If this is just a preprocessing step, I suggest you leave it at that. It is not something you need to prove. If for some reason you do want to dig into the problem, you could evaluate the effects of your methods through an external task as @lenz suggested.
How does external evaluation work?
When a task is too difficult to evaluate directly we use another task which is dependent on its output to draw conclusions about its success. In your case, it seems that you should pick a task that depends on individual words like document classification. Let's say that you have some sort of labels associated with your documents, say topics or types of news. Predicting these labels could be a legitimate way of evaluating the efficiency of your approaches. It is also a chance for you to see if they do more harm than good by comparing to the baseline of "dirty" data. Remember that it's about relative differences and the actual performance of the task is of no importance.
I am a graduate student focusing on ML and NLP. I have a lot of data (8 million lines) and the text is usually badly written and contains so many spelling mistakes.
So i must go through some text cleaning  and vectorizing. To do so, i considered two approaches:
First one:
cleaning text by replacing bad words using hunspell package which is a spell checker and morphological analyzer
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tokenization
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convert sentences to vectors using tf-idf
The problem here is that sometimes, Hunspell fails  to provide the correct word and changes the misspelled word with another word that don't have the same meaning. Furthermore, hunspell does not reconize acronyms or abbreviation (which are very important in my case) and tends to replace them.
Second approache:
tokenization
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using some embeddings methode (like word2vec) to convert words into vectors without cleaning text
I need to know if there is some (theoretical or empirical) way to compare this two approaches :)
Please do not hesitate to respond If you have any ideas to share, I'd love to discuss them with you.
Thank you in advance