If there is no corpse then there can be no class trial. If it takes a long time for the body to be discovered then the class trial will take place whenever the body is discovered, the game will have continued as normal until that point. The rules of the death game clearly outline the trigger condition for a class trial, Rule #9 (D2:GD) and Rule #11 (DV3:KH) "The Body Discovery Announcement will play as soon as three or more people discover a body for the first time" (This was not written in the rules in D1:THH but it was in effect regardless. Byakuya informs Makoto he missed it while passed out in Ch 1 and then it plays normally thereafter which is relevant in Ch 3). The body discovery announcement serves as the prelude to the investigation which leads into the class trial, it cannot be skipped.
This seems to conflict with a different rule in the rulebook Rule #7 (D1), Rule #5 (D2) and Rule #2 (DV3) phrased as "Once a murder takes place, a class trial will begin shortly thereafter. Participation is mandatory for all surviving students" in D1 and D2 but "Once a murder takes place, all surviving students must participate in a class trial" in DV3. The first phrasing implies that an investigation will trigger soon after the murder no matter what but this isn't even true within D1 (expanded upon below) and the DV3 phrasing better communicates the core of this rule, that being all surviving students must attend the class trial or else (although the consequences of missing the class trial are never explained).
The proof that there is no class trial without a body discovery announcement is integral to the plot of D1 spoilers for Trigger Happy Havoc:
In Ch 5 the body discovery announcement plays for the half blown up body of Mukuro Ikusaba, The Ultimate Soldier and "yet unseen" 16th student in the killing game. One would initially assume she had died just prior to the announcement but in actuality she was the first student killed. Mukuro was in cahoots with and posing as Junko Enoshima in the prologue but the actual Junko had decided rather than their agreed upon stunt of having a bunch of harpoon guns barely miss her to scare the students into fearing Monokuma to kill her for real before lowering her still breathing body into the floor where she died and was put into cold storage until Ch 5. A class trial was not held for Mukuro as this happened (presumably because the rule pertains to corpses and Mukuro hadn't died by the time she disappeared from view). It was only held in Ch 5 when her body was discovered. This says a few things, class trials do not need to follow the order of the murders (contradicting the rule saying a trial shortly follows a murder) but they do need to follow the order the bodies are discovered. A class trial is not held until the body is discovered which implies if a body is never found, no class trial is ever held. This makes sense in the framework the killing game, the only way to graduate is to kill another student, let the trial happen and not be voted guilty. Never having the body found is counterproductive. We also know from the alternate ending of Ch 5 that if nobody is murdered the remaining students never graduate and remain trapped in the school forever.
An additional note pertaining to what it means for a "body" to be discovered.
A half blown up body counts (D1 Ch 5)
A skeleton picked clean by piranhas counts (DV3 Ch 2)
Even a blood stain and sleeve sticking out from a hydraulic press counts (DV3 Ch 5).
This suggests that "evidence of a body" counts as a "body" for the purposes of the body discovery announcement. Whether this applies to a body thrown in an incinerator or a volcano is unclear, but again, a murder without any trace of a body is counterproductive to winning the game, if the body cannot trigger the body discovery announcement then the class trial needed to win will never happen.