Being correct and following the rules is generally a good thing in any endeavor. It gets tricky with grammar and writing for two primary reasons. First, the rules of grammar and writing can get pretty convoluted with exceptions and acceptable (but incorrect) common usage. In other words, saying or writing something correctly may actually seem anything but correct to a reader or listener. Second, we are generally willing to hear or read what a speaker or writer meant rather than expecting proper form and grammatical construction. In other words, because we don't want to be held to a perfect grammatical standard, we often overlook such errors in others. In truth, being understood is the most important thing; however, the judgments people make about how one speaks or writes are real and can have a real impact on a career or an issue of importance.
The answer to your post depends upon what it would mean for the writer to be effective. For example, if you are a political speech writer who needs to help a candidate "sell" himself to an educated audience, then correct grammar is essential.
Similarly, if you are writing for a test (such as an AP exam or the SAT), you would not be considered effective as a writer if you are guilty of multiple grammatical errors.
In contrast, dialect often includes slang, grammatical idiosyncrasies, and the like in order to establish characterization, theme, setting, etc. But even when a writer chooses to use dialect or slang, he or she must make sure that the meaning is clear in order for the work to be effective.
While I am not someone who listens for every grammatical error in someone's speech, I am bothered personally by speakers or writers using words incorrectly or committing numerous grammatical errors because it usually implies that that speaker is careless.
If a person uses incorrect grammar, they can still generally be an effective writer because their meaning can still be clear. For example, if someone were to write "I seen him coming down the street," it will annoy people like me, but the meaning is still clear.
Punctuation is more important. There is a book entitled Eats, Shoots, and Leaves. It is based on someone's sentence about a panda which "eats, shoots, and leaves." That first comma should not be there. When it is included, it makes it look like the panda eats, then shoots someone or something, and then leaves. This sort of mistake can make for actual problems in understanding what a writer is trying to say.
I realize that grammar and punctuation skills are not stressed as strongly in public schools today, and as a longtime English teacher, I find this practice unsettling. Looking at many of the eNotes questions posed by some users reflect a nearly unrecognizable use of the English language--filled with misspellings, incorrect grammar, run-on sentences and abbreviations. Part of the problem is today's use of texting and emails, where the norm seems to be to use as few capital letters and correctly spelled words as possible. Grammar and punctuation rules have some flexibility, but a flagrant disregard for proper usage--whether deliberately shortened or from a lack of knowledge--tends to show that the user is either lazy, unknowledgable or simply uncaring. Using incorrect grammar and punctuation is no different from mistating factual information or failing to follow other set rules: It shows a disregard for set standards, much in the same way a motorist breaks the rules of the road or a factory worker cuts corners in order to make things easier or finish faster. Most importantly, improper grammar usage and punctuation is often seen by others as a sign of limited understanding or intelligence. For example, a resume or cover letter filled with incorrect grammar usage when applying for a job is a sure way to let the prospective boss know to continue on to the next applicant. Correct grammar may not be necessary in everyday speech or even in many jobs, but using them correctly shows that you have taken the time to learn and understand an important aspect of education.