Do have somebody to look at the language/grammar you are using. But be aware of letting them write too much.
I have seen applications (for academic programs, but also for jobs) being tossed because of looking "too perfect", especially for non-native speakers. It is not a matter of the grammar being very good, it was a matter of the content "fitting too well", using all the expected buzzwords, and displaying a cultural sensitivity for the German job market/academic milieu a person with this biography could not have. This looks like it has been written by a ghostwriter, or copied from a "how to submit applications" book.
I guess that a person sending such an application still has the chance to get invited for an interview, if the running is not close. But when a prof is paring down a list, a person with this kind of application can get thrown out early, because the information he provides is disregarded as "he is telling me what he thinks I want to hear, and it might or might not be really true".
So, there is indeed a case of an application being too perfect to be regarded as real. And if you are a non native speaker, you are more likely to hit such a barrier than a native speaker, because the professor expects a bit less proficiency from you.
But this barrier comes long after the case which you are describing here. We are talking about the kind of application that can be written by somebody with knowledge not only of the language, but with the whole selection process and the country's and organisation type culture. If you express what you want to say in your best English, and somebody corrects your grammar and a few word choices, the chances that you come close to being regarded as "so perfect he must be fake" are astronomically small. So do let somebody edit your writing, it has advantages (described in the other answers) and it won't become good enough to disqualify you.