Can a person win a post-conviction case based on a traffic stop that should have been completed or suppressed?

You may seek a post-conviction relief petition on that basis, but whether it will be succesfful depends on a number of factors with the most important being whether it was previously litigated or discussed. 

It's possible, but usually not by arguing the stop itself. In Indiana post-conviction proceedings, issues that could have been raised at trial or on direct appeal, like a Fourth Amendment challenge to a traffic stop, are generally treated as waived. The post-conviction court won't simply revisit whether the evidence should have been suppressed.

The more common route is an ineffective assistance of counsel claim. If your trial lawyer never filed a motion to suppress, or failed to argue that the officer kept you longer than needed to handle the traffic violation (for example, holding you to wait for a drug dog, which the U.S. Supreme Court addressed in Rodriguez v. United States), that failure may be the basis for relief. To win, you generally must show that a suppression motion likely would have been granted and that there's a reasonable probability the outcome would have been different without that evidence. This is stronger when the stop produced the key evidence in the case, such as drugs, a weapon, or a chemical test.

Several factors matter a great deal. If you pleaded guilty, you'd typically need to show that your lawyer's failure affected your decision to plead and that you would have gone to trial instead. If the suppression issue was already raised and decided on direct appeal, it usually can't be relitigated. And while Indiana has no fixed deadline for filing a post-conviction petition, the State can argue unreasonable delay, and federal habeas has a one-year limit, so don't wait. An attorney who handles post-conviction work should review your trial record, including any police video, to evaluate the claim.