I agree with FYO about White bulking up and moving to RB/WR. In fact, when he was drafted, I remember predicting to Lil B and Brian (via IM) that he would be converted to RB, in order to run the wildcat.
Perhaps this will prove to be true, however I would recommend that you wait until after preseason next year to feel convicted about this. As far as I can recall, we have only seen him throw one real pass (barring some junk time in preseason). He may have snuck in a pass when I wasn't paying full attention.
I am predicting that the coaches will call on him to start passing soon, but if I am wrong and it doesn't happen this season I will be looking at what he does next preseason. By that point, if he appears to be severely lacking at passing proficiency I would start feeling convicted that he needs to be listed and used as something other than a QB.
This is likely what they are asking Pat White to do...
First, he must read the defense and make the proper check if necessary. He must determine whether the play should be run as a pass, run, sneak or option. After that he has to be able to run the play effectively. All of this must be learned and worked on in a secondary manner to what is happening with Henne (and Pennington before him). It sounds simple, but most young QBs are working on Pass and Run with a single (and simple) audible option between the two.
Now lets look at his progression...
First, he appeared to be given no option to change the play before the snap. He simply was used to hand off (and had one experimental deep play). Then he was given a second option to sneak the ball. Next, he appeared to be given a combonation of the ability to call a simple audible (not including pass) in which he could hand off, sneak, or run the option. This is where he is now. The next step will be to give him a few pass plays that he can check too. Once this happens, he can run, sneak, run option or pass. This is when he will start to become dangerous. Keep in mind that he will a significant lack of variability in each of those categories, but the fact that he can do so many different things alone will be all a defense can handle.
One final point...
Do you really think that this coaching staff has more faith in Ronnie and Ricky throwing the ball than Pat White? I assure you the answer is no. From what I have seen, this is the way Sparano works. He does not experiment on the field (although he likes to make you think he does). He wants to see it in practice and he wants to see it done right. The Ronnie and Ricky pass packages were likely installed well before White was on the team and have been practiced ever since. Furthermore, White has not fully been established as a significant running threat. Don't forget he is not a running back and will likely never be established as a significant running threat until he starts passing the ball.
Sorry for the long post, it was the only way I thought I could get the points across without confusion.