Would the announcement of penalty for blank answers in a test improve the global results of the class?
Usually the system goes like this: Good answer = get some points, no answer = no points, wrong answer = negative points.

Note that by this system, students who don't study a part of the material do get penalized by not getting any points, is just that the penalty is not as big as by guessing the wrong answer.

I do believe that this system works well as it is and would be wrong to penalize blank answers. The catch is that the system has to be designed in such a way that the expected value for random guessing should be lower than the expected value for no answers.

Here is why I think why negative blanks would be wrong:
In theory, the goal of the tests is to test what the students know and what they don't know. By encouraging them to leave blanks when they don't know the answer it becomes clear even to them what they do not know and what they know. 

Also, by forcing them to answer at random the grade of average and weak students becomes more a measure of luck than of knowledge. A weak student who guesses by luck 7 out of 12 answers will get more points than a student who doesn't know 6 answers but misses all 6 of them. 

And if you think that this is not relevant, ask yourself the following question: would you trust your doctor if he passed his classes by guessing the answers? Would you trust him if he diagnoses by randomly guessing? 

P.S. Just to clarify, the answer to your question depends by what you understand by "improved test results". For me the relevance of a test is to test the actual knowledge of the students, and a test result is good if there is a strong correlation between the knowledge and the result. In this sense, the test results would definitely not improve.

If by test results you understand the average score, then the scores would improve. But then, instead of doing this just give each student 100%, that would be the best test ever right? But then, the score of the "best test ever" would be completely irrelevant, and most likely useless (especially in the cases where the score is used for ranking i.e. admission, scholarships,..)