In most cases, yes you can. I know this from personal experience, because this has happened to me.
Since 1983, I have been working on and off in call centers as an outbound telemarketer, market research interviewer, telephone fundraiser, call center operator, and customer service representative. Most of them have been hired by other companies to do their various sales, marketing, research, and customer service projects.
They monitor your calls and performance very closely to make sure that you are meeting the companies' and the clients' required production goals. If not, they'll either write you up, send you home, suspend you, and/or even fire you. These companies are in business to please their clients and to make money at the same time, and they'll do everything they can to protect their interests.
If they do fire you for unacceptable performance, you can certainly file for unemployment; as long as there was no wilful misconduct involved. You went in there when you were supposed to. You didn't goof off. You weren't insubordinate. You followed the companies other policies and procedures, and you tried you very best. You just didn't perform up to the company's standards, and that's the bottom line.
I too was let go from a lot of these jobs for the same reason. Because I tried my best, and of course, there was no willful misconduct involved, then yes: I was able to collect unemployment.
If you're ever fired for unacceptable performance, regardless of how hard you tried, don't be ashamed to go and file for umemployment. If they turn you down, then you have to right to appeal it. In most cases, you didn't do anything wrong. You just weren't cut out for the job that they hired you to do, and that's the bottom line.