Summary: yes, but use TrueCrypt instead.
From the documentation:
WinRAR offers you the benefit of industry strength archive encryption using AES (Advanced Encryption Standard) with a key of 128 bits.
So yes, the data is encrypted. This is only one of the elements of security, however. Another important element is how the key is derived from the password: what kind of key strengthening is performed? The slower the derivation of the key from the password, the more costly it is for an attacker to find the password (and hence the key) by brute force. A weak password is toast anyway, but good key strengthening can make the difference for a reasonably complex but still memorable password. WinRAR uses 262144 rounds of SHA-1 with a 64-bit salt, that's good key strengthening.
An academic paper has been written on the security of WinRAR: On the security of the WinRAR encryption feature by Gary S.-W. Yeo and Raphael C.-W. Phan (ISC'05). Quoting from the abstract (I haven't read the full text, it doesn't seem to be accessible without paying):
In this paper, we present several attacks on the encryption feature provided by the WinRAR compression software. These attacks are possible due to the subtlety in developing security software based on the integration of multiple cryptographic primitives. In other words, no matter how securely designed each primitive is, using them especially in association with other primitives does not always guarantee secure systems. Instead, time and again such a practice has shown to result in flawed systems. Our results, compared to recent attacks on WinZip by Kohno, show that WinRAR appears to offer slightly better security features.
The advantage of using the encryption built into the RAR format is that you can distribute an encrypted RAR archive to anyone with WinRAR, 7zip or other common software that supports the RAR format. For your use case, this is irrelevant. Therefore I recommend using a software that is dedicated to encryption.
The de facto standard since you're using Windows is TrueCrypt. TrueCrypt provides a virtual disk which is stored as an encrypted file. Not only is this more secure than WinRAR (I trust TrueCrypt, which is written with security in mind from day 1, far more than any product whose encryption is an ancillary feature), it is also more convenient: you mount the encrypted disk by providing your password, then you can open files on the disk transparently, and when you've finished you unmount the encrypted disk.
Out of curiousity can what someone writes in their journal be used to incriminate someone in court?
This depends on the jurisdiction, but in general, yes, as they say in the movies, anything you say or write can be used against you. You may be legally compelled to reveal encryption keys, and may face further charges if you refuse.