The short answer: No
The long answer: Also No
Here is why this does not hold water:
- Until recently we were not able to extract soft tissues recently as in last 10 years. This is to the best of my knowledge but the first discovery of soft tissue in dinosaurs was about 10 years ago by Mary Schweitzer.
- Most of the tissue is very old and it would be exceedingly rare for DNA to last that long (another ref and another one), so extracting enough DNA to run tests on it from a single fossil will be very challenging if not impossible. The DNA may degrade in ways we have not yet discovered due to the time variable.
- If anyone could successfully extract DNA and read it it would make them an instant star in the world of paleontology, biology, evolutionary science, and many other fields. I do not have a ref for this since it has not happened yet so I will give you the person who is rewinding chickens.
(Yes, it is a google search but this shows the fame / notoriety he has for something that is similar to this subject).
- Scientists are unlikely to shy away from this simply to the prospect that it may break a current model of evolution that is generally accepted. Infact this may be a driving force. Scientists are like that - where ground breaking discoveries that overturn the way we currently see our world, are kind of golden prizes to scientists (E.g. there is a lot of excitement about faster than light neutrinos or gravity waves or this list)
So no, this idea does not hold much water if any. The only reason I can see for paleontologists to not attempt to extract DNA is the amount of material they would need to destroy for an infinitesimally small chance of getting reliable data (ref above for half life of DNA). I suspect they much rather wait a hundred years till something gets made to scan the fossil molecule by molecule.
These people are not extracting dinosaur dna but it's still research into extracting ancient dna from once living creatures: Absence of Ancient DNA in Sub-Fossil Insect Inclusions Preserved in ‘Anthropocene’ Colombian Copal.
If its too long or too technical then the very last paragraph sums it up pretty well.