Yes the cop can ticket you without showing you the readout on the radar. More importantly, if you were to take this to trial, a jury could convict you of speeding even if the officer testified he didn't even have a radar. Police are trained in a technique called pacing whereby they match (or attempt to match) the speed of the car they are observing. They can then testify that they found the speed to be a certain number.
You can certainly argue that the only reason you committed the failure to signal intent violation was that the officer was right off your bumper (and maybe even attribute the speeding to him following you so closely). The right argument may convince the jury that there is not proof beyond a reasonable doubt or that even if there is, that his behavior necessitated you violating the law.
You can always try this case yourself (or negotiate with the prosecutor yourself) but you may want to consider hiring a criminal defense attorney to represent you. He or she should be well-versed in the Texas Rules of Evidence and cross-examination and may be able to present a convincing case for your innocence to a jury.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.
Yes the officer can issue you a citation without showing you the radar readout.
Check with a lawyer in your locale to discuss more of the details.
Good luck to you.
NOTE: This answer is made available by the out-of-state lawyer for educational purposes only. By using or participating in this site you understand that there is no attorney client privilege between you and the attorney responding. This site should not be used as a substitute for competent legal advice from a licensed professional attorney that practices in the subject practice discipline and with whom you have an attorney client relationship along with all the privileges that relationship provides. The law changes frequently and varies from jurisdiction to jurisdiction. The information and materials provided are general in nature, and may not apply to a specific factual or legal circumstance described in the question.