No, they do not. Most of them are dismissed with prejudice before even an Answer to the Complaint is filed. You have a right to file a pro se lawsuit in Federal court, after paying the
filing fee and after paying a process server to serve the Complaint as service of a Complaint is not something one is allowed to do on his own.
With the exception of certain appeals by prisoners, which fall under a different set of rules, and with the exception of civil actions which are clearly frivolous or otherwise incapable of amendment, a pro se action in a civil rights case is allowed to file one amended complaint as a matter of course to correct any pleading defects in his initially filed Complaint. Unless the Amended Complaint is dismissed with prejudice for a hyper technical reason (such as omitting to state "42 U.S.C. 1983" in the jurisdiction and venue section of the Complaint) or the judge creates his own pleading barrier not found in the Federal Rules of Civil Procedure and dismisses the case with prejudice then that is typically the end of the line for most pro se cases.
One can file an appeal as a matter of right (after paying the $505 filing fee AND filing a timely notice of appeal (correctly worded)) but the court of appeals will look at his Complaint and almost invariably conclude that it is incapable of amendment and affirm the dismissal with prejudice.
If by "hearing" you meant a trial then again no. Trials take place at the very end of a civil lawsuit and the trial process itself is fraught with procedural landmines in addition to the procedural landmines which have to be sidestepped en route to the trial.
FYI, as a matter of course in the Federal Central District of California, motion hearings (such as a motion to dismiss with prejudice) don't take place. There is no right to a motion hearing under the Federal Rules of Civil Procedure. The decision on whether or not there will be a motion hearing is left entirely in the hands of the judge.
Forget everything you have ever seen on TV or at the movies about our justice system. They bear absolutely no resemblance to reality.