It may go a long way towards discrediting jungle primaries. As it was, the 1991 LA-GOV election was long held up as an example of the problems with Louisiana's primary system, since the general election candidates were very nearly the two worst conceivable candidates: a former governor who had been hounded out of office four years previously on charges of bribery and mail fraud (*) combined with dismal perceived job performance, and a Klan leader. Heck, when Edwards lost the previous election, one newspaper ran an editorial saying that the only way Edwards could win an election in the future would be if his opponent were Adolf Hitler.
(*) He was tried and acquitted in federal court during his previous term as governor, but was widely viewed as having gotten off on a technicality. After his OTL final term as governor, he was tried again on new charges and convicted of 17 counts of fraud, extortion, and racketeering.
If Duke wins rather than Edwards, I'd expect the election to have even more impact and staying power as a negative example. We probably wouldn't see Washington and California adopt jungle primaries in 2008 and 2010 respectively, and we might see Louisiana abolish their jungle primary.
As for Duke's term in office, I wouldn't be surprised to see him not last a full term. Louisiana's constitution has provisions for recall elections, which if I'm reading them correctly mean that the Louisiana state legislature could pass a law providing for any rules they want for triggering a recall election for governor, after which there'd be a yes/no vote on removing Duke from office. If "yes" gets a majority, Duke is out and the Lieutenant Governor (Melinda Schwegmann (D) IOTL, although butterflies might lead to Paul Hardy (R) being reelected instead) serves out the remainder of his term. I'd expect almost every member of the legislature and a solid majority of the electorate to strongly prefer either Schwegmann or Hardy over Duke, and Governor Duke would be widely seen as a major embarrassment for the state.
Of course, it depends what the POD is. I've been assuming it was something along the lines of Edwards being caught red-handed taking mob payoffs or knocking over liquor stores, making it hard for people to stomach voting for him even to keep Duke out. If the POD is instead a massive groundswell of pro-Klan sentiment, all bets are off.