Sure will.
The trash is actually just a folder in your home directory called
.Trash. The dot in front hides the folder so that you don't actually see it. Let's try removing files with a bash command (Terminal). Open up Terminal (/Applications/Utilities/) and execute the following (type each and press enter):
This will move you into the .Trash folder (much like double-clicking on a folder in Finder). Now, execute the following:
This will list all the files in the folder which should be familiar to you (this is the contents of your Trash). Now, to remove the files, execute the following:
This will remove the files in that directory, do it recursively (through all the folders) and will force it if there are permission issues.
You don't need to securely empty the trash unless you always delete sensitive information. It takes much longer and like I just mentioned, is only really needed if you want there to be no chance of recovery.