Interesting question!
If Nimoy hadn't come back, there would've been no need to do most of the plot of the STIII we got. So Spock wouldn't only be merely dead, he'd really be most sincerely dead. So no McCoy going nutty from Spock's
Katra. Spock's "Remember" only amounted to McCoy's line "He isn't really dead, as long as we remember him" at the end of TWOK. No need for Sarek to return and tell Kirk that Spock's Katra is missing. No stealing of the
Enterprise to recover Spock's body from Genesis, and consequently, no destruction of the
Enterprise. And no need for Kirk and his crew to defy Starfleet orders and become fugitives and refugees on Vulcan. And no reason to kill off David, either.
They could definitely follow up on Genesis somehow, especially if Carol and David Marcus were to play a substantial role in the film. I'd imagine that Genesis could be stable in this reality, as there'd be no need to get rid of it without it having the power to resurrect the dead. So perhaps there could be a plotline that continued the debate over the ethics of Genesis, or they could still have the Klingons or the Romulans try to use it as a weapon.
And without Nimoy directing and Spock staying dead, perhaps they could've gotten Nicholas Meyer to return as writer & director. Meyer coming back increases the chances of Kirstie Alley returning as Saavik, continuing her original characterization. Maybe this time around her dual Vulcan/Romulan heritage could've made it into the final cut.
With no Spock, I think there'd definitely be more investment in the new characters of Saavik and David. David could join Starfleet eventually, to make plotting future movies easier if nothing else. Let's say he becomes a junior science officer to help replace Spock. And I'd imagine they could introduce a few more new characters as well, and give us a more organic transition into a new generation of
Star Trek. TWOK already introduced and killed off a nephew for Scotty, but perhaps protégés for McCoy, Sulu, Uhura, and Chekov could've been introduced.
I wonder if any follow ups would've been TV movies instead of theatrical releases, though. After all, with
Star Trek's most popular character gone, Paramount might've wanted to hedge their bets and keep the costs low. And if the newer cast proved popular enough, we could've gotten a new regular TV series featuring them taking over the
Enterprise.
I just hope the new series wouldn't spill over into 1987, though, because I'd hate for Kirstie Alley not to be available to take over for Shelley Long on
Cheers. 