I personally think that it should be (though my definition of pressure is that there is somebody watching), though I'm biased - I have the same problem.
I am an experienced programmer, and I have also done my share of programming under pressure (e.g., in academic environments such as solving a final exam as an undergrad or teaching as a grad) and believe I did it fairly well. However, I find that when I am writing code while somebody is watching my every tiny move, it is extremely distracting and I fail even the trivial stuff.
In my case, I try to figure out what the interviewer is thinking, and I keep looking for little tells. This is fine for Hold'em, where you have two cards to look at, but not so fine for programming.
Also, I personally tend to initially write with crappy syntax (on a whiteboard) and then fix little things, rather than do a clear line-by-line. Again, in an interview, that's a problem because I am worried that as soon as I don't close that brace or add the semicolon, I will look bad.
In addition, I often find "think aloud" to be distracting. This is acceptable in pair programming, but not in individual programming.
Furthermore, I have been in interviews where while I am writing, the two interviewers keep chatting between them on how they solve the same problem. Imagine that you are trying to code while two other people are reading each other's code aloud to the same problem. This is among the "scare the interviewee techniques".
Finally, some people don't do well with paper or with whiteboard. I am one of them. I like knowing that I can insert lines easily and type at the speed that I think. When I am confronted by a whiteboard or paper, it takes me ages to handwrite, and in my case I also can't really read my handwriting so everything is trickier. Give me a computer and I'll do fine.
So in a nutshell, my view is this: Wanting to make sure your interviewee perform under pressure is a very good idea. Time limits are also a very good idea. However, your prospective hire will never have to code with someone looking over his shoulder like that.
Therefore, give him the task, tell him you'll be back in 20 minutes, and then get the hell out of there!!!. Leave them alone. Give them a phone number for questions or for letting you know when they're done.
Note that I do agree with Drew that it's important to isolate the person from the aid of Google and code samples. I don't consider that pressure, though.