Is it ok to call the professor in this situation?
First, ask yourself whether you are sending the right email.

One of my professor mentors had a very useful heuristic for ensuring effective communication with busy people.  For any busy person, email typically gets triaged into three bins:


Email that can be safely ignored.
Email that can be responded to with trivial effort, thereby clearing it from their "todo list."
Email that requires non-trivial effort to respond, and must be put off for later... and later may be a long time, because now it's competing with their other "large" duties.


If you want a response from a busy person, write a short email that includes precisely one question, and make sure that question is easy to respond to.  For example, in your case, if you send email saying:


  Here is my research proposal, as discussed.  Can you please send me feedback?


then that might get no response until the professor has the feedback ready, and preparing your feedback may get pushed off and pushed off again.  The professor might also misremember the deadline and have a lesser sense of urgency.
If instead you write:


  Here is my research proposal, as discussed.  Please recall that I must submit before the deadline of XXX, and I would like time to revise if necessary.  When can I expect your feedback?


In this you've posed an easy question, which should get a response, and also gotten them to commit to a specific date.  If you don't get a response in a day or two from an "easy" email like this, then you need to wonder whether this person is actually somebody you want to work with.

What, however, if you send the right email, get them to commit to a date, and then they fail to either respond or tell you they need more time?  At that point, I would recommend against either emailing or calling on the phone.  Instead, go find the professor in person.  I have found that with busy people who fail on their commitments, that finding them in person is the best way to get yourself back in their queue.  Again, however, you should ask yourself whether you really want your whole Ph.D. to be this way, because it is likely to be a pattern...