Yes, I have done this many times. I always fight all of my traffic tickets in Texas and just plead not guilty.
The closer I get to trial date the more anxious my prosecutors are to settle, and they'll usually come up with better and better deals the closer to trial they get. Sometimes trials take 2 or more years to come up. (Texas has weird 'speedy trial' laws in which you have to request and demand a speedy trial)
If you can get the prosecutor to agree to deferred adjudication then take the deal to the court and the judge will most likely give it to you.
Some judges will let you take the defensive driving even after pleading not guilty but I am not sure you'd get that one.