Manual tests and unit tests are designed for different purposes*, so the answer is "yes" - substituting one for the other is a dangerous practice.
Unit tests pin down your assumptions about your code in the form of assertions that you make throughout your tests. Along with automated integration tests, unit tests help ensure that your software does what you think it should do. When done correctly, they should give you a high level of confidence in the correctness of your software. Automated testing is not as time-consuming, and much less error-prone.
However, it is often impractical to eliminate all manual testing. Specific areas of concern include integration with other products that you must use, such as installers, web browsers, and operating systems. At the minimum, someone needs to install your product before shipping, and see if it starts up, or open your product in the browser to see if the visuals remain in the right places. All of that can be automated, but the effort to make it happen does not make it worth the trouble, especially since we are talking about running through a ten-minute checklist.
If we are talking about the specific "manual tests vs. unit tests" distinction, the two concepts do not slice the space of software testing in the same dimension: in addition to unit tests, you need integration tests, regression tests, and stress tests. These are usually automated, but they can be done manually. Moreover, even the unit testing can be done manually with a small help of a software driver. That's why substituting one for the other is not a good comparison: if your manual testing covers unit testing, regression testing, stress testing, and integration testing, then replacing it with automated unit testing is not a fair exchange. If the gap is filled with some other mean of automated testing, then you can shift some burden from the manual testing to unit testing, but you would not be able to eliminate manual testing completely.
As Jimmy Hoffa
correctly notes, there are companies who (mis)use manual testing in the areas where unit testing is a lot more appropriate. In cases like that, switching to unit tests is not dangerous - in fact, it is highly desirable.