Nope.  `setStackTrace` looks like the following:

```java
    public void setStackTrace(StackTraceElement[] stackTrace) {
        // Validate argument
        StackTraceElement[] defensiveCopy = stackTrace.clone();
        for (int i = 0; i < defensiveCopy.length; i++) {
            if (defensiveCopy[i] == null)
                throw new NullPointerException("stackTrace[" + i + "]");
        }

        synchronized (this) {
            if (this.stackTrace == null && // Immutable stack
                backtrace == null) // Test for out of protocol state
                return;
            this.stackTrace = defensiveCopy;
        }
    }
```

What it does is basically to deep-copy an array of `StackTraceElement`.  `StackTraceElement` does not keep `Class`:

```java
public final class StackTraceElement implements java.io.Serializable {
    // Normally initialized by VM (public constructor added in 1.5)
    private String declaringClass;
    private String methodName;
    private String fileName;
    private int    lineNumber;
...
```

For more information, check the OpenJDK source code.