No, because often on a mobile device, the user can be temporarily distracted and attention can be sporadic. Mobile users multitask more often.

For this reason, you don't want to have to put the onus on the user to remember where they came from (in order to make the decision of where they want to go next).

In any case a back button on a mobile device can be confused with the back button on the device itself.

A better way to think of it is to add a Done button on the page, which whilst it might do the same thing as the back button, actually aligns better with the user's thought processes - ie I'm done here, take it away and put me somewhere useful to move on

In addition, by making the 'Back' button the only way out, you effectively have led the user up a dead end, leaving them to back out. Never block the user - always make them feel like they are progressing forward, not having to backtrack. Do this by always giving navigation options relevant to the scenario they find themselves in.

Update - websites and native apps:

I think it's worth saying that there is a distinction between standalone apps, and websites (as displayed in a browser). By websites, I mean website pages, web apps, and websites that behave like apps.

For native apps where the browser is not the interface to the device, then as others have pointed out, you would need some method of adhering to the expected design and behaviour that users will be used to using with other apps on their device.

I deliberately worded that last sentence carefully because if for example on iOS you need a back button on your app, you should look at the design guidelines, as even re-positioning the back button to an unexpected position or making it look different to how users expect could throw them completely.